Inverted Linear Quadtree: Efficient Top KSpatial Keyword Search

Chengyuan Zhang†, Ying Zhang†, Wenjie Zhang†, Xuemin Lin† ‡

† The University Of New South Wales, Australia

‡ East China Normal University, China

{zhangc, yingz, zhangw, lxue}@cse.unsw.edu.au

Abstract—With advances in geo-positioning technologies andgeo-location services, there are a rapidly growing amount ofspatio-textual objects collected in many applications such aslocation based services and social networks, in which an objectis described by its spatial location and a set of keywords (terms).Consequently, the study of spatial keyword search which exploresboth location and textual description of the objects has attractedgreat attention from the commercial organizations and researchcommunities. In the paper, we study the problem of top k spatialkeyword search (TOPK-SK), which is fundamental in the spatialkeyword queries. Given a set of spatio-textual objects, a querylocation and a set of query keywords, the top k spatial keywordsearch retrieves the closest k objects each of which contains allkeywords in the query. Based on the inverted index and the linearquadtree, we propose a novel index structure, called invertedlinear quadtree (IL-Quadtree), which is carefully designed toexploit both spatial and keyword based pruning techniques toeffectively reduce the search space. An efficient algorithm is thendeveloped to tackle top k spatial keyword search. In addition,we show that the IL-Quadtree technique can also be applied toimprove the performance of other spatial keyword queries such asthe direction-aware top k spatial keyword search and the spatio-textual ranking query. Comprehensive experiments on real andsynthetic data clearly demonstrate the efficiency of our methods.

I. INTRODUCTION

With the increasing pervasiveness of the geo-positioningtechnologies and geo-location services, there are anenormous amount of spatio-textual objects available inmany applications. For instance, in the local search service,online business directory (e.g., yellow pages) provides thelocation information as well as short descriptions of thebusinesses (e.g., hotels, restaurants). In the GPS navigationsystem, a POI (point of interest) is a geographically anchoredpushpin that someone may find useful or interesting, which isusually annotated with texture information (e.g., descriptionsand users’ reviews). Moreover, in many social networkservices (e.g., Facebook, Flickr), a huge number of geo-tagged photographs are accumulated everyday, which can begeo-tagged by users, GPS-enabled smartphones or cameraswith a built-in GPS receiver (e.g., Panasonic Lumix DMC-TZ10). These uploaded photographs are usually associatedwith multiple text labels. As a result, in recent years variousspatial keyword query models and techniques have emergedsuch that users can effectively exploit both spatial and textualinformation of these spatio-textual objects.

In the paper, we investigate the problem of conductingtop k spatial keyword search (TOPK-SK) [1], [2]; that is,given a set of spatio-textual objects, a query location q and

a set of keywords, we aim to retrieve the k closest objectseach of which contains all keywords in the query. The topk spatial keyword search is fundamental in spatial keywordqueries and has a wide spectrum of applications. Below aretwo motivating examples.

q

p1

p3

( pizza,coffee, sushi )

p2 ( pizza,coffee, steak )

( pizza, sushi )

( coffee, sushi )

p4

( pizza, steak,seafood )p5

Fig. 1. Online Yellow Pages Example

In Fig. 1, suppose there are a set of businesses whoselocations (represented by squares) and service lists (a set ofkeywords) are registered in the online yellow pages of a localsearch service provider. When a GPS-enabled smartphone userwants to find a nearby restaurant to have a piece of pizza anda cup of coffee, she may send the local search server two key-words, coffee and pizza. Based on the user’s current location(e.g., the point q in Fig. 1) derived from the smartphone andthe two query keywords, business p1 is returned by the server.Note that although businesses p3 and p4 are closer to q thanp1, they do not satisfy the keyword constraint.

In another example, suppose a traveler wants to take somephotos of nearby mountains at the sunset around a touristattraction. Based on her location and the scene she wantsto capture (mountain and sunset), a TOPK-SK query onthe geo-tagged photographs uploaded by other visitors canprovide some useful suggestions.

Motivation. As stressed in [1], [2], the performance ofthe spatial keyword query is poor if objects are separatelyorganized by textual index and spatial index. Therefore, themain challenge is how to effectively combine the spatial indexand textual index such that a large number of non-promisingobjects can be effectively eliminated from the candidate setbased on both the spatial proximity and keyword constraint.

To facilitate the TOPK-SK query, two index structures areproposed in the literature: inverted R-tree [1] and informationretrieve R-tree (IR2-tree) [2]. For each keyword t, the invertedR-tree technique builds an R-tree for objects in which t

978-1-4673-4910-9/13/$31.00 © 2013 IEEE ICDE Conference 2013901

appears, and hence objects which do not contain any querykeyword can be immediately eliminated in the TOPK-SKquery. The inverted R-tree based technique is efficient whenthe number of keywords is small. However, the performanceof the inverted R-tree based technique significantly degradeswhen the number of keywords in the query grows because itdoes not exploit the AND semantics in the query, i.e., prune anobject if it does not contain all query keywords. The IR2-treetechnique [2] alleviates this issue by utilizing the signaturetechnique; that is, we can decide if we should further explorea node based on a small summary of the keywords appearingin the objects contained by the node. Nevertheless, accordingto our analysis in Section III-A, the fact that all spatio-textualobjects are organized in a single R-tree may seriously impairthe performance of the search algorithms.

Our empirical study shows that other existing spatialkeyword indexing techniques (e.g., IR-tree [3], [4], KR∗-tree [5] and WIR-tree [6]), which are proposed for slightlydifferent spatial keyword search problems, cannot efficientlysupport the problem of top k spatial keyword search either.That is because, same as IR2-tree, all objects are organizedin a single R-tree in these techniques.

In the paper, we propose the inverted linear quadtree(IL-Quadtree) indexing technique which naturally combinesthe advantages of inverted R-tree and IR2-tree techniques.Specifically, for each keyword we build a linear quadtree forthe related objects so that the objects which do not containany query keyword can be immediately excluded fromcomputation. Besides facilitating spatial search, the quadtreefor each keyword can also serve as the signature of the objectsin the sense that we can effectively prune a group of objectsbased on the AND semantics. Moreover, as the space fillingcurve technique is employed by the linear quadtree, the objectsare clustered on the disk based on their spatial proximity,which enhances the I/O efficiency of our search algorithm.

Contributions. Our contributions can be summarized asfollows.

• To facilitate the top k spatial keyword search (TOPK-SK),we propose a novel indexing structure called IL-Quadtreeto effectively organize spatio-textual objects.

• Based on IL-Quadtree, we develop an efficient top k spatialkeyword search algorithm.

• We show that IL-Quadtree can also efficiently support thedirection-aware top k spatial keyword search and spatialkeyword ranking query.

• Comprehensive experiments demonstrate the efficiency ofour methods.

Roadmap. The rest of the paper is organized as follows.Section II formally defines the problem of top k spatialkeyword search, followed by the introduction of the relatedwork. Section III presents the IL-Quadtree structure. Efficienttop k keyword search algorithm is proposed in Section IV andpossible extensions of the IL-Quadtree index are discussed inSection V. Experimental results are reported in Section VI.Section VII concludes the paper.

II. PRELIMINARY

In this section, we first formally define the problem oftop k spatial keyword search, and then introduce the relatedwork. Table I below summarizes the mathematical notationsused throughout this paper.

Notation Definition

o (q) a spatio-textual object (query)o.loc(q.loc) location of the object o (query q)

o.T a set of keywords used to describe oq.T a set of query keywords for query qV , v vocabulary, size of the vocabulary

t a keyword (term) in Vl the number of query keywords in q.Tn the number of spatio-textual objectsm the average number of keywords in each objectno the number of objects within the search regionps the average surviving probability of the objects

within the search regionδ(p1, p2) the distance between points p1 and p2

δmin(R, p2) the minimal distance between the region R and point p2

e a node of an R-tree or quadtreeseq(e) the split sequence of a quadtree node

w maximal depth of IL-Quadtreew′ minimal depth of the black leaf node in IL-Quadtreec split threshold for a node in IL-Quadtree

TABLE ITHE SUMMARY OF NOTATIONS.

A. Problem Definition

In the paper, a spatio-textual object o is described bya spatial point in a two dimensional space and a set ofkeywords (terms) from the vocabulary V , denoted by o.locand o.T respectively. A top k spatial keyword query, denotedby q, consists of a natural number k, a query location and aset of query keywords. The problem of top k spatial keywordsearch (TOPK-SK) is formally defined as follows.

q

p1

p3

p2

p4

p5

p6

p7

p8

(t1,t2)

(t1,t2)

(t1,t3)

(t1)

(t2,t3)

(t3)

(t3)

(t2,t3)

p9(t3)

k=1,q, q.T=

TOPK-SK query

s r

(t1)p10(t2)p11

{ t1,t2 }

Fig. 2. Example of TOPK-SK query

Problem Statement. Given a set O of spatio-textual objects,a query object q where q.loc is the query location and q.T isa set of query keywords, we aim to find the closest k objectseach of which contains all of the query keywords. We assumeties are broken arbitrarily in the paper.

In the paper hereafter, whenever there is no ambiguity,“spatio-textual object” is abbreviated to “object” and o (q) isused to represent its location o.loc (q.loc).

Example 1: In Fig. 2, there are a set of spatio-textualobjects {p1, . . . , p11}. A user located at the point q wants to

902

find the nearest object (i.e.,k = 1) which contains keywordst1 and t2 (i.e., q.T = {t1, t2}). Fig. 2 shows that the objectretrieved by the TOPK-SK query is p1. Objects p3, p4, p7,p8 and p5 are eliminated due to the keyword constraint.

B. Related Work

In this subsection, we first present two existing techniques,inverted R-tree and IR2-tree, for the problem of TOPK-SKquery as well as some other top k queries dealing with bothspatial and texture information. Then other types of spatialkeyword queries are introduced. We also present detailsof some related techniques which can be adopted to theTOPK-SK query.Inverted R-tree

The inverted index technique has been extensively appliedin various information retrieval applications. For eachkeyword (term) t, a set of objects (e.g., files and documents)containing t are kept in a list. Given the fact that the numberof keywords input by the user is usually small in practice,the inverted index technique can efficiently support keywordsearch since only a few lists need to be loaded and the targetobjects can be identified by merging the lists.

To efficiently facilitate the spatial keyword search, it isfairly natural to employ the spatial index techniques toorganize the objects for each keyword, instead of keepingthem in a list. Then, for a given TOPK-SK query, wecan simultaneously apply the incremental nearest neighborsearch [7] on the related spatial indices until k objectssatisfying the keyword constraint are retrieved. The invertedgrid index is proposed in [8], [9], [10] to organize objects foreach keyword. Considering that the grid index does not scalewell towards the location skewness of the objects, [1] proposesthe inverted R-tree technique. For each keyword t ∈ V , anR-tree is constructed for the objects in which t appears.

Following is an example of the inverted R-tree.Example 2: Given a set of objects as shown in Fig. 2 where

V = {t1, t2, t3}, Fig. 3 shows that three R-trees R1, R2 andR3 are constructed based on the related objects for t1, t2 andt3 respectively. For the TOPK-SK query in Fig. 2, the objectsaccessed in inverted R-tree based technique are p3, p4, p5 andp1 in order. Here, an object is accessed if it is within the searchregion and is loaded in the computation. Note that althoughthe objects p7 and p8 are also within the search region, noneof them is accessed as they are not contained in R1 or R2.

p1 p2 p3 p4 p10

E1 E2

R1 ( t1 )

p1 p6 p2 p5

E1 E2

R2 ( t2 )

p3 p5 p6 p7

E1 E2

R3 ( t3 )

p8 p9p11

Fig. 3. Example of inverted R-tree

IR2-treeIntuitively, the inverted R-tree is efficient when there is only

one query keyword since we only need to issue a k nearestneighbor search on the corresponding R-tree. Nevertheless,the performance of the inverted R-tree significantly degradesagainst the number of keywords l in the query. This isbecause the search region of the TOPK-SK query will enlarge

against the number of keywords, i.e., an object is less likelyto contain all query keywords in T when l increases, and allobjects which contain at least one keyword and are withinthe search region will be visited.

Motivated by this, Felipe et al. propose the informationretrieval R-tree (IR2-tree) structure [2] which can alleviateabove issue by utilizing the signature technique. Supposeobjects are organized by an R-tree according to their spatiallocations, a signature (i.e., a fixed-length bitmap) is put toeach node of R-tree, which summarizes the set of keywordscontained by its descendent data entries (objects). Morespecifically, suppose each keyword is mapped to a particularposition of the signature, e.g., by applying hash functionon the keyword, the i-th bit of the signature of a node isset to one if any of the keywords contained by the objectsin the node is mapped to i. Clearly, the signature of anintermediate IR2-tree node is the bitwise-OR of its childentries’ signatures. During the query processing, we do notneed to further explore an IR2-tree node if its signatureconfirms that none of the objects in the node contains allquery keywords, and hence the I/O cost can be saved.

p4 p710 01

p6 p901 01

E1 E2

11 01

p10 p1110 01

E3

11

E7 E8

11 11

p8 p501 01

p211

E4 E5

01 11

E9

11

E11 E12

11 11

p1 p311 11

E6

11E1 E2 E3

E4 E5 E6

E7 E8

E10

11E9 E10

E11 E12

Fig. 4. Example of IR2-tree

Example 3: Regarding the objects in Fig. 2, assume thateach signature (bitmap) has two bits, and keywords t1, t2and t3 are mapped to the first, the second and the secondpositions of the bitmap respectively, Fig. 4 illustrates theIR2-tree entries and their corresponding signatures. For theTOPK-SK query in Fig. 2, although there are totally 6 objectswithin the search region, we only access 4 objects p3, p4, p7

and p1 in order because the entry E4 can be eliminated basedon its signature, and hence the accesses of p5 and p8 can beavoided. Note that, although none of the objects in E1 (p4

and p7) satisfies the keywords constraint, E1 is loaded dueto the false positive incurred.

Variants of the top k spatial keyword search.Besides the top k spatial keyword search, there are many

important variants in the literature with different focus.Instead of applying the keyword constraint, the spatialkeyword ranking query [3], [4], [11] is proposed to rankobjects based on a scoring function which considers thedistance to the query location as well as the textual relevanceto the query keywords. In [3], [4], the information R-tree(IR-Tree) structure is proposed to support the spatial keywordranking query, which is similar to the IR2-tree technique.Based on the inverted R-tree, the spatial inverted Index (S2I)structure is proposed in [11], where an aggregate R-tree isemployed to organize objects for each keyword.

903

In [12], Li et al. study the problem of top k spatial keywordsearch in which the direction constraint is considered.Effective direction-aware index structure is proposed toprune the search space. To facilitate the joint processing ofmultiple TOPK-SK queries, the WIR-tree is proposed in [6]following the framework of IR-tree. Other variants includelocation-aware type ahead search [13], top k spatial keywordsearch on road network [14], etc.

Other Spatial Keyword related Queries.Besides the top k query, other types of spatial keyword

queries have also attracted much attention in the literature.Given a search region, the spatial keyword search is studiedin [8], [9], [5], [10] which aims to efficiently identify theobjects which satisfy both spatial and keyword constraints; thatis, each retrieved object falls in the search region and containsall query keywords. Specifically, the inverted grid index tech-nique is employed in [8], [9], [10] where a grid index is usedto organize the related objects for each keyword. The KR∗-treeis presented in [5]. The inverted R-tree [1] can also supportthe region based spatial keyword search. In [15] and [16], theproblem of the spatial keyword ranking query within a searchregion is studied, where various tf-idf based ranking functionsare proposed. In [17], Li et al. investigate the problem of spa-tial approximate string search. To explore the spatial relation-ship among the candidate objects, Zhang et al. [18] study theproblem of m-closest keyword search which retrieves spatiallyclosest objects matching m keywords. Chao et al. [19] investi-gate the problem of k collective keyword search. Very recently,assuming the spatial extent of the objects are regions, Fan el al.study the problem of spatio-textual similarity search in [20].Details of the IR-tree, KR∗-tree and WIR-tree

Although the above-mentioned IR-tree, KR∗-tree andWIR-tree techniques are designed to tackle slightly differentproblems, they can be easily adopted to support top kspatial keyword search. Below, we provide some detailedintroduction for these techniques, which will be evaluated inour empirical study.IR-tree. In [3], [4], the information R-tree (IR-tree) structureis proposed to support the spatial keyword ranking query,which is similar to the IR2-tree technique. The main differenceis that, instead of the signature, an inverted file is maintainedfor each node which maintains the keywords and the relatedinformation for objects contained by the node. Some optimiza-tions are applied to further improve the query performanceby taking advantage of the tree construction methods.

p4 p7 p11

E1 E2

E5 E6

E1 E2

E5

p6 p9 p8 p5 p2

E3 E4

E3

E6

p1 p3

E4(t1:p4) (t3:p7)

InvFile(E 1)

InvFile(E 2)

(t2:p6 , p11) (t3:p6 , p9)

InvFile(E 3)

(t1:p2 ) (t2:p2 , p5)

InvFile(E 5)

(t2: E2) (t3:E1, E2 )(t1:E1)

(t3:p5 , p8)

(t1:p1,p3,p10 ) (t2:p1)

InvFile(E 4)

(t3:p3)

(t1:E3,E4 )

InvFile(E 6)

(t2:E3,E4)

E7

p10

(t3:E3,E4)

Fig. 5. Example of IR-tree

Example 4: Suppose the objects in Fig. 2 are organized

by the IR-tree as shown in Fig. 5 1. Same as the Example 3,there are 6 objects in the search region. Nevertheless, we onlyaccess 4 objects p3, p8, p5 and p1 in order because the entryE1 can be eliminated based on inverted file InvF ile(E1).WIR-tree. WIR-tree is proposed in [6] to efficiently support abatch of TOPK-SK queries. The structure of WIR-tree tree isthe same as the IR-tree where all objects are organized by oneaugmented R-tree. The main difference is that the constructionof WIR-tree takes advantage of the term frequencies of thekeywords to facilitate the joint TOPK-SK queries. Morespecifically, the objects will be recursively partitioned into 2h

groups for given h most frequent terms t1, . . . , th. In the i-thiteration, objects in a group g will be divided into two groupsg1 and g2 where objects in g1 contain ti and objects in g2 donot. Then WIR-tree is constructed based on these groups.

E1 , E3 , E4 , E5 , E6, E7t1

t2 E2 , E3 , E4 , E5 , E6, E7

t3 E1 ,E2 , E3 , E4 , E5 , E6, E7

E6

R-tree

Fig. 6. Example of KR∗-tree

KR∗-tree. In [5], Hariharan et al. propose the KR∗-treestructure to process the region based spatial keyword search.KR∗-tree is similar to IR-tree in the sense that objects are firstorganized by one R-tree and then inverted index techniquesare applied. As shown in Fig. 6, for each keyword t, an R-treeentry e is kept in the list if t appears in any objects containedby e. Regarding the example in Fig. 2, KR∗-tree has thesame R-tree structure as the IR-tree (Fig. 5). In Fig. 6, theentry lists of keywords t1, t2 and t3 are illustrated. Same asExample 3, p4 and p7 can be eliminated because entry E1

does not appear in the entry list of t2.

III. IL-QUADTREE

In this section, we introduce a new indexing mechanismcalled inverted linear quadtree (IL-Quadtree) for the top kspatial keyword search. In Section III-A we describe theshortcomings of the existing indexing approaches. To addressthese shortcomings, Section III-B proposes the inverted linearquadtree based index structure.

A. Motivation

In this subsection, we first conduct performance analysisbased on some assumptions to intuitively demonstrate theadvantages and disadvantages of the existing techniques.Then we present some important properties for an indexingstructure supporting TOPK-SK query.

Since the incremental nearest neighbor search is appliedin the existing works, they have the same search region; thatis, the radius of the search region centered at q (e.g., sr inFig. 2) grows until finding k objects satisfying keywordsconstraint. Recall that we say an object is accessed if it iswithin the search region and is loaded in the main memory.

1We do not show the term frequency related aggregate information inIR-tree since we do not need these information for TOPK-SK query.

904

In the sequel, we evaluate the performance of inverted R-treeand IR2-tree by estimating the number of objects accessedduring the search, denoted by sn, because the cost modelderived is simple and can provide some useful insights. Letno and ps denote the number of objects within the searchregion and the average surviving probability of these objects(i.e., an object within the search region is expected to beloaded with probability ps), respectively. Clearly, we havesn = no × ps. Below, we will analyze the performance oftwo techniques in the aspects of no and ps values.

Assume n objects are uniformly distributed in two dimen-sional space [0, 1]2, and there are m keywords for each objectwhich are randomly picked up (with replacement) from thevocabulary V with size v. For a given TOPK-SK query with lkeywords, the probability that an object contains all query key-words is (m

v )l. Therefore, the number of objects in the searchregion (no) is expected to be k×( v

m )l. Let sr denote the radiusof the search region, with the same rationale in [7] we have

sr =

√k × ( v

m )l

π × n(1)

Inverted R-tree. According to the uniform assumption,for each keyword ti ∈ V , there are n×m

v objects in itscorresponding R-tree Ri. Since only the objects containing atleast one keyword in q.T are accessed, it is immediate that

sn = no = l × π × s2r ×

n × m

v(2)

= l × k × (v

m)l−1 (3)

As shown in Equation 3, we have sn = k when l = 1,i.e., there is only one query keyword, which is the optimalsolution in terms of the number of objects accessed. However,sn grows exponentially against the number of keywords l inthe TOPK-SK query because the number of objects withinthe search region (no) grows quickly but none of them canbe eliminated (i.e., ps = 1). Therefore, the inverted R-treebased technique performs poor when l increases.IR2-tree. In [2], an object will be loaded in the mainmemory if all of its descendent entries satisfy the conjunctioncondition. Here, we only need to consider the signatures forthe leaf nodes because the signatures on higher level do notenhance the filtering capability although they may speed upthe filtering process. Given the sr in Equation 1, the expectednumber of objects within the search region, denoted by no,equals k × ( v

m )l. Let np, ne and nL denote the page size,the entry size and the length of each signature (bitmap), thecapability of each IR2-tree node, denoted by nc, is � np

ne+nL�.

Now, we assume objects are organized by no

ncgroups (i.e., leaf

nodes). For each group, let p denote the surviving probabilityof a group, i.e., the probability that the signature satisfies thekeyword constraint. In [2], a group survives the test if the lcorresponding bits are hit in the signature (bitmap)2. Given

2For the simplicity of the cost model, we assume l keywords are mappedto different bits.

a group of nc objects and each object is described by mkeywords, a bit of the signature is set with probability nc×m

nL.

Then, we have p = (nc×mnL

)l. Consequently, the expectednumber of objects visited (sn) is

sn =no

nc× p × nc = no × p (4)

= k × (v

m)l × (

m × nc

nL)l (5)

As shown in Equation 5, the probability p (ps = p) de-creases exponentially regarding l. Therefore, compared to theinverted R-tree method (Equation 3), Equation 5 implies thatthe IR2-tree technique might be less sensitive to the number ofquery keywords l if the costs incurred by the enlarged searchregion can be compensated by the enhanced pruning capability.

Despite its advantage, IR2-tree technique is less efficientthan inverted R-tree based one when the number of keywordis small. As shown in Equation 3 and Equation 5, we haveno equals l × k × ( v

m )l−1 and k × ( vm )l for inverted R-tree

and IR2-tree techniques respectively. This implies that muchmore objects are involved in the search region in IR2-treebased methods since m×l

v � 1 in practice. Therefore, asconfirmed in our initial empirical study, inverted R-treealways outperforms IR2-tree when l is small although asignificant amount of objects can be pruned. Moreover, as asingle tree is constructed for all objects, IR2-tree techniquecannot properly capture the distribution of objects regardingeach individual keyword. In other existing techniques suchas IR-tree, WIR-tree and KR∗-tree, the objects are alsoorganized by a single augmented R-tree. This implies thatthey inevitably suffer from the same problems.

Above observations motivate us to develop a new indexstructure so that we may have a small number of objects withinthe search region (i.e., small no) as well as the ability to pruneobjects within the search region (i.e., small ps). Firstly, it isdesirable to develop a new index structure which falls in thecategory of inverted index, i.e., related objects are organizedby a spatial index for each keyword, so that the objectswhich do not contain any query keyword can be immediatelyeliminated. Secondly, the new index structure should beadaptive to the distribution of the objects for each keyword.Thirdly, we need to exploit the AND semantic, i.e., pruning agroup of objects which do not satisfy the keyword constraint.

Unlike IR2-tree which applies the signature technique onthe keyword, we can build the signatures based on the spacepartition for each keyword so that a group of objects can beeliminated based on their signature. Given a region R in thespace, let si be an indicator where si is set true if there isat least an object containing keyword ti, and si is set falseotherwise. Obviously, we do not need to explore any objectwithin R if any of the si is set false and ti ∈ q.T since noneof these objects satisfies the conjunction condition. Here, si

is the signature of the region R regarding keyword ti, whichcan be represented by one bit.

We can enforce the inverted R-tree technique to exploitthe AND semantics by issuing a range query on other relatedR-tree. However, this cannot pay-off the high checking cost.

905

NW

SW

NE

SE(00) (01)

(10) (11)

(a) (b)

SW

0 1

p1

2 3p2 p3

p4

SE NW NE

(c)

4

8 12

0 1 2 3

4 8 12

(0, p 2 ) (1, p 3) (3, p 1 ) (12, p 4)

(d)

B+ tree

Fig. 7. Linear Quadtree Example

On the other hand, the inverted grid index technique [8],[9], [10] can be naturally extended to utilize the signaturetechnique. More specifically, as the space is partitioned intocells by the grid index, for each keyword ti ∈ V we can useone bit as the signature of a cell. Our empirical study showsthis can significantly improve the performance. However, thegrid index technique does not scale well towards the skewnessof the objects, which is common in many real applications.

In the paper, we adopt the linear quadtree structure becausethe quadtree is more flexible in the sense that the indexis adaptive to the distribution of the objects and we mayprune the objects at high levels of the quadtree. Clearly, thenew structure proposed satisfies the above-mentioned threeimportant criteria of the spatial keyword indexing method.

B. IL-Quadtree Structure

A quadtree is a space partitioning tree data structure inwhich a d-dimensional space is recursively subdivided into2d regions. Due to its simplicity and regularity, the quadtreetechnique has been widely applied in many applications.As an efficient implementation of the disk-based quadtree,the linear quadtree [21] is proposed to keep the non-emptyleaf node of the quadtree in an auxiliary disk-based onedimensional structure (e.g., B+ tree), where each node can beencoded by the space filling curve techniques (e.g., Mortoncode [22], Hilbert code and gray code [23]).

In the paper, we encode the quadtree nodes based on theMorton code [22] (a.k.a. Z-order) because the Morton codeof a node is encoded based on its split sequence, i.e., thepath of the node in the quadtree, and the code of a particularnode (region) in the space is unique. This is essential becausemultiple quadtrees with different shapes are used in the paper.

Now we describe how to derive the Morton code of a nodebased on its split sequence in 2-dimensional space. As shownin Fig. 7(a), assuming that quadtrees resulting from a split arenumbered in the order SW, SE, NW and NE, which are repre-sented by 00, 01, 10 and 11 respectively 3. Then the code canbe derived by concatenating the split codes in each subdivision.For example, Fig. 7(b) and Fig. 7(c) show the space partitionand the corresponding tree structure of a simple quadtree for agiven set of points {p1, . . . , p4} where leaf nodes are labelledby their Morton codes. As shown in Fig. 7(c), in the paper, weuse a circle and a square to denote the non-leaf node and leaf

3Note that SW is the abbreviation of South-West. Similar definition goesto SE, NW and NE.

node respectively. Moreover, a leaf node is set black if it isnot empty, i.e., it contains at least one point. Otherwise, it is awhite leaf node. Suppose the maximal depth of the quadtree is2, the split sequence of the node 1 is “SW, SE” and hence itscode is represented by 0001. For the node at higher level, weuse 0 to pad the remaining binary digits. For instance, the splitsequence of the node 12 is “NE” and its code is represented by1100 where the last two binary digits are padding. In Fig. 7(b)and (c), the codes of the leaf nodes are labelled by the corre-sponding integer number of their split sequences (i.e, Mortoncode). Note that in the paper the quadtree structure is kept asthe space partition based signature of the objects, and hencethe level of a node in the quadtree is available during the queryprocessing. Consequently, we can come up with the correctnode (region) based on the code and the level information.

For the linear quadtree, we only keep the black leaf nodeson the disk by one dimensional index structure (e.g., B+

tree), which are ordered by their Morton codes. Fig. 7(d)shows an ordering results of these black leaf nodes as wellas the objects resident on them, where the node codes arerepresented as integer numbers.

LQ 1

q

0 1

2 3

4

8 12 13

14 15

LQ 2

q

0 1

2 3

4

8 12

10

p1

p3

p2

9

11

p5

p2

p6

p1p4

p10p11

Fig. 8. Example of IL-Quadtree

IL-Quadtree. In the paper, for each keyword ti ∈ V we builda linear quadtree, denoted by LQi, for the objects whichcontain the keyword ti. Besides the black leaf nodes, wealso explicitly keep the quadtree structure, which serves asthe signature of the objects in LQi, which can be easily fitinto the main memory. More specifically, a bit is kept foreach node of the quadtree, which is set to 1 for black leafnodes and non-leaf nodes and 0 otherwise. Obviously, a node

906

in LQi is empty (i.e., it does not contain any object withkeyword ti) if the bit is set to 0. Regarding the objects inExample 1 (Fig. 2), Fig. 8 illustrates the linear quadtrees LQ1

and LQ2 constructed for keywords t1 and t2 respectively.Recall that the leaf nodes are labeled by their Morton codes.Index Maintenance. For an incoming new object o, it willbe inserted into the corresponding linear quadtrees basedon its textual information. Particularly, a leaf node of thequadtree is split if it contains more than c objects and it doesnot reach the maximal depth w which is the pre-determinedmaximal partition level. As to the deletion, an object o will beremoved from its corresponding linear quadtrees. Meanwhile,some of the cells may be merged due to the deletion. For theeffectiveness of the signatures, we enforce that all objects arepushed to the black leaf node below the level w′ (minimalpartition level) because a black leaf node at high level mayimpair the pruning capability.

IV. IL-QUADTREE BASED TOPK-SK QUERY

In this section, we introduce an efficient TOPK-SKquery algorithm assuming that objects are organized by anIL-Quadtree. Same as other inverted index based approaches,we also conduct incremental nearest neighbor search on theIL-Quadtree. The main difference is that we can make use ofthe space partition based signatures (i.e., quadtree structures)to eliminate non-promising objects. Example 5 below showsthe motivation of our algorithm.

Example 5: Given the TOPK-SK query as shown in Exam-ple 1 (Fig. 2) where the query point is q, q.T = {t1, t2} andk = 1, the search region of IL-Quadtree based technique isthe same as the search region of the inverted R-tree and IR2-tree techniques. Only objects p4 and p1 will be accessed inour example. Objects p7 and p8 are immediately eliminatedbecause they do not appear in LQ1 or LQ2. Moreover, we donot need to explore cell 3 in LQ1 because cell 3 in LQ2

is empty, and hence p3 is eliminated. Similarly, p5 is notaccessed as well. Note that we access p4 because cell 8 in LQ1

overlaps cell 10 in LQ2, and both of them are black leaf nodes.Algorithm 1 illustrates the details of the IL-Quadtree based

TOPK-SK query. A min heap H is employed to keep thequadtree nodes where the key of a node is its minimal distanceto q, denoted by δmin(e, q). Let I(q.T ) denote a subset of{1, . . . , v} such that i ∈ I(q.T ) if the keyword ti is a querykeyword. In Line 3, the root nodes of the related quadtreesare pushed into the heap H. Each node e popped in Line 5 isprocessed as follows. For a black leaf node e of the keywordti, if there are more than one keyword in q.T (i.e., l > 1)we need to decide if the objects within e should be loaded bytesting the signatures of the quadtrees of other query keywords(Line 9). More specifically, based on the Morton code (i.e.,split sequence) of the node e, we can quickly find out if e isoverlapped with another black leaf node of LQj . Following thesplit sequence of e, we claim that none of the objects satisfiesthe keyword constraint if a white leaf node in LQj is encoun-tered. If the node e passes these l− 1 tests (Line 10), Line 11loads the objects contained by e. We keep a counter for each

object o, denoted by ohit and Line 13 increases it by one. A setR is employed to keep the k closest objects seen so far, whichsatisfy the keyword constraint, and the distance threshold λrepresents the k-th closest distance in R. Lines 13-16 calculatethe distance between the object o and q and update R and λ ifthe counter of o reaches l, i.e., o contains all query keywords.When the popped node e is a non-leaf node (Line 17), a childnode e′ of e will be pushed to H if it is not a white leafnode and the minimal distance between e′ and q, denoted byδmin(e′, q), is not larger than λ (Line 18-20). The algorithmterminates when H is empty and the results are kept in R.

Algorithm 1: TOPK-SK (Q, q, k)Input : LQ : the IL-Quadtree, q : the spatio-textual query

k : number of objects returned,Output : R : TOPK-SK query result.R := ∅; H = ∅; λ =∞ ;1for each LQi where i ∈ I(q.T ) do2

Push root node of R into H ;3

while H �= ∅ do4e← the quadtree node popped from H ;5if e is a black leaf node then6

Suppose e is from LQi;7for each LQj where j �= i and j ∈ I(q.T ) do8

CheckSignature(e, LQj ) ;9

if e passed the signature test then10Load objects contained by e;11for each object o contained by e do12

ohit := ohit + 1 ;13if ohit = l then14

Compute δ(o, q) ;15Update λ and R ;16

else if e is a non-leaf node then17

for each child node e′ of e do18if e is19

not a white leaf node and δmin(e′, q) ≤ λ thenPush e′ into H ;20

return R21

Correctness. We first show the correctness of the signaturecheck. For any object o in a quadtree LQj , o must resideon a black leaf node. Therefore, given a black leaf node e inLQi, it is immediate that we do not need to explore objectsin e if there is another quadtree LQj where j ∈ I(q.T ) andnone of the black leaf nodes of LQj overlaps e. Accordingto the construction of the quadtree, if e overlaps a node e′ inLQj , it will imply that seq(e) ⊆ seq(e′) or seq(e′) ⊆ seq(e)where seq(e) is the split sequence of the node e. As shown inFig. 9, there are three cases for a given split sequence seq(e)and quadtree LQj: (i) encounter a white node (Fig. 9(a)),(ii) encounter a black node (Fig. 9(b)) and (iii) end up at anon-leaf node (Fig. 9(c)). Clearly, the occurrence of the case(i) implies that we do not need to explore e since none ofthe black leaf nodes in LQj overlaps the node e. Otherwise,cases (ii) and (iii) indicate that there exists a black leaf nodein LQj which overlaps e. Therefore, the correctness of oursignature follows. Secondly, we show that it is safe to prune

907

a node e′ if δmin(e′, q) > λ. This is immediate because thenodes of the quadtrees are accessed in non-decreasing orderaccording to their minimal distances to q.

seq(e)= 0011

00

11

(a)

00

11

(b)

00

11

(c)

Fig. 9. signature Check

Time Complexity. Suppose there are no objects within thesearch region of the algorithm, the heap size is at most l×no

and hence the heap maintenance cost is log(l × no) for eachnode in the worst case where none of the objects is pruned(Line 20). The signature checking cost is (l − 1) × w foreach node at Line 9 and hence the total checking cost isno × (l − 1) × w in the worst case, where w is the maximaldepth of the quadtree. As to each object o, it takes O(1) timeto find and increase its counter (ohit) supposing that accessedobjects are kept in a hash table. Therefore, in the worse case,the computational time of Algorithm 1 is O(l×no × (log(l×no) + l × w)). In the empirical study, the performance of thealgorithm is highly efficient as a large number of objects andquadtree nodes are eliminated by making use of distance basedpruning and signature based pruning techniques.

V. SUPPORT OTHER SPATIAL KEYWORD QUERIES

IL-Quadtree can also support other types of spatial keywordqueries. In the paper, we focus on the direction-aware topk spatial keyword search and the spatial keyword rankingqueries.

qp1

p3

( pizza,coffee, sushi )

p2 ( pizza,coffee, steak )

(pizza, sushi )

(coffee, sushi)

p4

( pizza, steak,seafood )

p5

αβ

(a) (b)q

αβ

R1

R2

R3

R4

Fig. 10. Direction-aware top k spatial keyword search

A. Direction-aware top k spatial keyword search

As discussed in [12], in some applications users may beinterested in the direction-aware top k spatial keyword search;that is, besides the keyword constraint, the candidate objectsmust fall in a particular direction regarding the query q. Asshown in Fig. 10(a), suppose query keywords are coffee andpizza and query direction constraint is described by [α, β](i.e., the shaded area), the object p2 is the nearest object whichsatisfies both keyword and direction constraint. Note that p1

is not a candidate object because of the direction constraint.

Let angle(o, q) denote the angle of the object o regardingthe query q, the problem of direction-aware top k spatialkeyword search is formally defined as follows.

Problem Definition. Given a set O of objects, a query qwith direction constraint [α, β], we aim to retrieve k closestobjects {o} such that each object o satisfies both keywordand direction constraints; that is, o.T constains all keywordsin q.T and α ≤ angle(o, q) ≤ β.

Algorithm 1 in Section IV can be easily extended tosupport the direction-aware top k search by verifying directionconstraint for the objects and quadtree nodes at Line 12 and 19of Algorithm 1 respectively. It is trivial to check the directionconstraint for an object. We show how to efficiently check thedirection constraint for a rectangular region (quadtree node).Particularly, we say a region R fully satisfies the directionconstraint if all points within R meet the direction constraint.And R does not satisfy the direction constraint if none ofthe points in R meets the direction constraint. Otherwise,R partially satisfies the direction constraint. As shown inFig. 10(b), we have R1 fully satisfies the direction constraint,R2 partially satisfies the direction constraint, and R3 and R4

do not satisfy the direction constraint.Clearly, we can prune a quadtree node if it does not satisfy

the direction constraint. The qudatree node e and all ofits descent nodes satisfy the direction constraint if e fullysatisfies the direction constraint. We need to further check thedirection constraint for its child nodes or objects contained ifthe node partially satisfies the direction constraint.

B. Spatial Keyword based Ranking

In some applications such as location based web documentssearch, the textual information of an object may be describedby a bag of keywords, and it is desirable to evaluate thetextual relevance between an object and the query based onsome ranking functions in the field of information retrieval.In this subsection, we first introduce how to rank objectsbased on both the spatial proximity and the textual relevance.Then an efficient ranking algorithm is presented based on aslight modification of IL-Quadtree.

Definition 1: Spatial proximity fs(q, o). Let δmax denotethe maximal distance in the space, the spatial relevancebetween the query q and the object o, denoted by fs(q, o), isdefined as δ(q.loc,o.loc)

δmax.

Same as [3], we adopt the language model based functionto measure the textual relevance of the objects regarding thequery q, which is defined as follows.

Definition 2: Textual relevance ft(q, o). Let wt,o denotethe weight of the keyword t regarding object o, and

wt,o = (1 − ξ)tft,o

|o.T | + ξtft,D

|D| , (6)

where tft,o and tft,D are the term frequency of t in o.Tand D respectively. Here, D represents the text informationof all objects in O and ξ is a smoothing parameter. Then thetextual relevance between q and o is defined as follows.

ft(q, o) = 1 −∏

t∈q.T wt,o

maxP(7)

908

where maxP is used for normalization.Based on the spatial proximity and textual relevance

between the query and the object, the spatio-textualranking score of an object o regarding the query q canbe defined as follows.

Definition 3: spatio-textual ranking score f(q, o). Letα be the parameter used to balance the importance of thespatial proximity and textual relevancy, we have f(q, o)= α × fs(q, o) +(1 − α) × ft(q, o). Note that the objectswith small score values are preferred (i,e., ranked higher).

Problem Definition. Given a query q and a set O of objects,we aim to find the top k spatio-textual objects with smallestspatio-textual ranking score values regarding Q.

Aggregate IL-Quadtree. To efficiently support the spatialkeyword ranking query, we slightly argument the IL-Quadtreeby hierarchically maintaining the keyword weight informationin the IL-Quadtree. For each quadtree node, instead of usingone bit to indicate whether there is any object within the node,we keep the maximal keywords weight among the objectswithin the node, which is named aggregate IL-Quadtree inthe paper.

Based on the definition of the spatio-textual ranking score,the following lemma is immediate, which implies that we maycome up with the lower bound of the ranking score value for anobject due to the monotonic property of the scoring function.

Lemma 1: Given two objects o and p, we say o is domi-nated by p regarding a query q if δ(o, q) ≥ δ(p, q) and wt,o ≤wt,p for every keyword t ∈ q.T , we have f(o, q) ≥ f(p, q).

The following Theorem is immediate based on Lemma 1,which implies that we may avoid accessing objects in a partic-ular region based on the aggregated term weight information.

Theorem 1: Given a region R in the space, for eachkeyword ti ∈ q.T , we use fi(R) to denote the maximal termweight of the objects within the region. Suppose we have anobject p where δ(p, q) = δmin(R, q) and wti,p = fi(R) fori ∈ I(q.T ), then for any object o within R, f(p, q) ≤ f(o, q).

Spatial Keyword Ranking Algorithm. We suppose objectsare organized by an aggregate IL-Quadtree, denoted by aLQ.Let Q be a virtual quadtree and a node e in Q is a leaf noderegarding the query q if for each keyword ti ∈ q.T there is ablack leaf node e′ in aLQi such that seq(e) ⊆ seq(e′); that is,for a leaf node e in Q, none of the corresponding nodes (i.e.,nodes with the same split sequence as e) is a non-leaf node.

Algorithm 2 illustrates the details of the aggregate IL-Quadtree based spatial keyword ranking approach where Theo-rem 1 is used to prune non-promising objects and the best-firstparadigm is adopted. Similar to the signature check in Algo-rithm 1, we can quickly identify the maximal term weights fora node e, i.e., fi(e) for any i ∈ I(q.T ), based on the split se-quence of e. Then, a lower bound of the ranking score value forall objects within e, denoted by f(e, q), can be derived basedon Theorem 1 at Line 11. Meanwhile, f(e, q) serves as the keyof a node e in the min heap H (Line 12). Similarly, the rankscore of an object regarding q is its key in H ( Line 19). Thealgorithm terminates when k best objects are visited (Line 7).

Algorithm 2: SK-RANKING (aLQ, k, q)Input : aLQ : the aggregate IL-Quadtree,

k : number of objects returned, q : the queryOutput : R : k objects with highest scoresR := ∅; H = ∅;1Push root node of the virtual quadtree Q into H ;2while H �= ∅ do3

e← the tuple popped from H ;4if e is an object then5R := R∪ e ;6Terminate the Loop if |R| = k ;7

else8if e is not a leaf node then9

for each child entry e′ do10

Compute f(e′, q);11

Push e′ into H ;12

else13C := ∅ ;14for each quadtree aLQi where i ∈ I(q.T ) do15

e′ ← the black16

leaf node in aLQi with seq(e′) ⊆ seq(e) ;C := C∪ objects in e′;17

for each object o ∈ C do18Compute f(o, q) and push it to H ;19

return R20

VI. PERFORMANCE EVALUATION

We present results of a comprehensive performance studyto evaluate the efficiency and scalability of the proposedtechniques in the paper. Especially, the following algorithmsare evaluated for the TOPK-SK query.

• ILQ IL-Quadtree based TOPK-SK algorithm proposed inSection IV.

• IVR The inverted R-tree based TOPK-SK algorithm [1].• MIR2 The enhanced IR2-tree technique [2] based TOPK-

SK algorithm.• KR TOPK-SK algorithm developed based on the KR∗-

tree [5].• WIR WIR-tree technique proposed in [6].• IR ,CM-CDIR IR-tree is proposed in [3] and CM-CDIR [4]

is one of its optimized variants.

Note that WIR technique [6] can immediately supportTOPK-SK query by issuing one query each time. Otherindexing techniques (KR, IR and CM-CDIR) can be easilyadopted by applying the incremental nearest neighbor searchand conducting keyword constraint verification against eachtree node visited.

Datasets. Performance of various algorithms are evaluated onboth real and synthetic datasets. The following four datasetsare employed in the experiments. Real spatial dataset GN isobtained from the US Board on Geographic Names4 in whicheach object is associated with a geographic location and a shorttext description. GN serves as the default dataset in the experi-ments. We also generate datasets Tigers and Cars by obtaining

4http://geonames.usgs.gov

909

the spatial locations from corresponding spatial datasets fromRtree-Portal 5 and randomly geo-tagging these objects withuser-generated textual content from 20 Newsgroups 6. To in-vestigate the scalability of the algorithms, we also include thesynthetic dataset SYN. A number of objects are randomly cho-sen from Cars dataset, and their corresponding keywords areobtained from a vocabulary whose term frequencies follow thezipf distribution where the parameter z varies from 0.9 to 1.3with default value 1.1. By default, the number of objects (n),the vocabulary size (v) and the number of keywords per object(m) are set to 1 million, 100 thousands and 15 respectively.Table II summaries the important statistics of four datasets.

Property Tigers SYN GN Cars

number of objects (millions) 0.56 1 2.2 2.25vocabulary size (thousands) 78 100 208 81

avg. number of keywords per obj. 14.878 15 6.75 26

TABLE IIDATASET DETAILS

0.05

0.1

0.15

4 8 16 32 64 128

Res

pons

e T

ime

(s)

Varying c

w’=7w’=8w’=9

w’=10w’=11

Fig. 11. Tuning IL-Quadtree

0

0.2

0.4

0.6

0.8

1 2 3 4 5

Res

pons

e T

ime

(s)

Varying l

GridGrid+SIG

ILQ

Fig. 12. Comparison with Grid

Workload. A workload for the TOPK-SK query consists of200 queries, and the average query response time and theaverage number of disk accessed are employed to evaluatethe performance of the algorithms. The query locations arerandomly selected from the underlying dataset. On the otherhand, the likelihood of a keyword t being chosen as querykeyword is freq(t)P

ti∈V freq(ti)where freq(t) is the term frequency

of t in the dataset. The number of query keywords (l) variesfrom 1 to 5, and the number of results (k) grows from 10 to50. By default, l and k are set to 3 and 10 respectively.

All algorithms in the experiments are implemented inJava. The source codes of IR and CM-CDIR [4] are publicavailable, and other algorithms are implemented basedon the data structures (e.g., R-tree and B+ tree) in thatsource code package. Experiments are run on a PC withIntel Xeon 2.40GHz dual CPU and 4G memory runningDebian Linux. All index structures are disk resident, and thepage size is fixed to 4096 bytes. We assume it takes 2msfor each disk access. For a fair comparison, we tune theimportant parameters of the competitor algorithms for theirbest performance. Particularly, for MIR2 the bitmap lengthat the leaf node is set to 4160, 5120, 5120 and 7680 bits forTigers, SYN, GN and Cars respectively. The parameter β andthe number of clusters are set to 0.1 and 20 for CM-CDIR.

5http://www.rtreeportal.org6http://people.csail.mit.edu/jrennie/20Newsgroups

A. Evaluating TOPK-SK query

Tuning IL-Quadtree. In all experiments, the maximalpartition level of IL-Quadtree (w) is set to 16. In Fig 11, wetune the performance of ILQ Algorithm by varying minimaldepth of the black leaf node (w′) and the split threshold(c). It is reported that different values of w′ and c have nosignificant impact on the performance when w′ < 11 andc > 16 in the settings. In the experiments, we set w′ = 8 andc = 64 for all datasets.Comparison with Inverted Grid Index. In Fig. 12,Algorithm Grid is the implementation of inverted indextechnique in [10], which does not utilize any signaturetechnique. As expected, the performance of Grid degradessignificantly with the increase of the number of querykeywords (l) since there is no pruning technique for objectswithin the search region. As discussed in Section III-A,Algorithm Grid+SIG is the extension of Grid by utilizingthe space partition based signature technique. It significantlyenhances the performance of Grid. Nevertheless, itsperformance is dominated by IL-Quadtree because Grid+SIGcannot capture the objects distribution for each keyword.Evaluation on different datasets. We investigate the queryresponse time, index construction time and index size of 7algorithms against four datasets Tigers, SYN, GN and Cars,where other parameters are set to default values. In Fig. 13(a),ILQ demonstrates superior performance in comparison withother algorithms. Fig. 13(b) depicts the index sizes occupiedby the algorithms. Particularly, KR has the smallest indexsize among the algorithms since only the R-tree entryidentifications are kept for each keyword as shown in Fig. 6.On the other hand, CM-CDIR has the largest index size dueto the extra clusters information kept. The construction timeof the index structures is depicted in Fig. 13(c). In the restof this subsection, we exclude IR and CM-CDIR from theperformance comparison as both of them are dominated byMIR2 and KR under all settings.Effect of the number of query keywords (l). We evaluatethe effect of the number of query keywords in Fig. 14. Recallthat the performance of the algorithms can be measuredby no × ps in the cost analysis of Section III-A, where no

is the number of the related objects covered by the searchregion and ps is the average surviving probability of theseno objects. Clearly, the growth of l will enlarge the searchregion, and hence leads to a larger no. On the other hand,the pruning capability of the algorithms will increase due tothe tighter keyword constraint, i.e., smaller ps.

Based on Fig. 14, we can make the following observations.

• ILQ and IVR. As only the objects containing at least onequery keyword may contribute to no in ILQ and IVR,they have the best performance when l = 1 under allsettings. As expected, the performance of IVR degradesdramatically when l grows due to the lack of ability toprune objects. It is reported that the performance of ILQ ismuch more scalable by making use of the space partitionbased signature technique.

910

10-2

10-1

100

101

102

TIGER SYN GN CARS

Res

pons

e T

ime

(s)

(a) Response Time

10-1

100

101

102

TIGER SYN GN CARS

Inde

x S

ize

(GB

)

(b) Index Size

100

101

102

103

TIGER SYN GN CARS

Con

stru

ctio

n T

ime

(min

)

(c) Index Construction Time

Fig. 13. Performance over Various Datasets

ILQ IVR MIR2 KR WIR

10-2

10-1

100

101

102

1 2 3 4 5

Res

pons

e T

ime(

s)

(a) Varying l on Tigers

10-2

10-1

100

101

102

1 2 3 4 5

Res

pons

e T

ime(

s)

(b) Varying l on SYN

10-2

10-1

100

101

1 2 3 4 5

Res

pons

e T

ime(

s)

(c) Varying l on GN

10-2

10-1

100

101

102

103

1 2 3 4 5

Res

pons

e T

ime(

s)

(d) Varying l on Cars

Fig. 14. Effect of the the number of query keywords (l)

ILQ IVR MIR2 KR WIR

10-1

100

101

102

10 20 30 40 50

Res

pons

e T

ime(

s)

k

(a) Response time, Tigers

101

102

103

104

105

10 20 30 40 50

# I/O

k

(b) I/O, Tigers

10-2

10-1

100

101

10 20 30 40 50

Res

pons

e T

ime(

s)

k

(c) Response time, GN

101

102

103

10 20 30 40 50

# I/O

k

(d) I/O, GN

Fig. 15. Effect of k

ILQ IVR MIR2 KR WIR

10-1

100

101

102

0.9 1.0 1.1 1.2 1.3

Res

pons

e T

ime

(s)

(a) Varying z

10-1

100

101

102

0.5M 1M 1.5M 2M

Res

pons

e T

ime

(s)

(b) Varying n

10-1

100

101

102

15 20 30 40 50

Res

pons

e T

ime

(s)

(c) Varying m

10-1

100

101

102

20k 40k 60k 80k 100k

Res

pons

e T

ime

(s)

(d) Varying v

Fig. 16. Effect of term frequency skewness (z), number of objects (n), number of keywords per object (m) and vocabulary size (v)

• MIR2 and KR. It is interesting that when l grows, theperformance of MIR2 and KR degrades significantlyon datasets Tigers (Fig. 14(a)), SYN (Fig. 14(b)) andCars (Fig. 14(d)), while it becomes better on dataset GN(Fig. 14(c)). This is because the locations of many objectswith high-frequency terms are closely clustered in datasetGN, and hence the growth of the search region is veryslow regarding l. Therefore, the extra cost invoked byenlarging the search region can be easily compensated bythe improved pruning capability on dataset GN. Recallthat all objects within the search region contribute to no

for MIR2, KR and WIR. Therefore, the number of objectsinvolved are likely to grow quickly regarding l, which is thecase regarding datasets Tigers, SYN and Cars, and hencethe performance of MIR2 and KR is seriously deterioratedby the increase of l in Fig. 14(a), 14(b) and 14(d).

• WIR. The trend of WIR is quite different to other

algorithms, where the performance is significantly enhancedwhen the number of query keywords grows. This is becausethe construction of WIR-tree relies on the keyword partitionand hence can take great advantage of a large numberof query keywords. However, the performance of WIR isdisappointing on all datasets when l is small. The reasonis that the construction of WIR may impair the spatialcloseness of the objects within the same node of WIR-tree.

Effect of the number of results (k). Fig. 15 reports thequery response time and the number of I/O accesses of thealgorithms as a function of k on two datasets Tigers andGN. As expected, the performance of all algorithms degradesregarding the increase of k (i.e., the larger search region).Compared with Fig. 14, the growth of the searching cost ismuch slower, specially for the GN dataset.Effect of the term frequency skewness (z). In Fig. 16(a),we evaluate the impact of the term frequency skewness on

911

the algorithms, where z varies from 0.9 to 1.3. As a querykeyword is selected based on the term frequencies, the searchregion of the algorithms shrinks when z increases, and hencethe performance of the algorithms (except WIR) improveswhen z is large. A keyword t with extremely high termfrequency is not in favor of WIR-tree construction becauseit is hard to evenly partition a group. This leads to the poorperformance of WIR when z increases.

Effect of n, m and v. Fig. 16(b), Fig. 16(c) and Fig. 16(d)report the query response time of the algorithms as a functionof the number of objects (n), the average number of keywordsper object (m), and the vocabulary size (v). It is shown thatthe performance of IL-Quadtree is quite scalable against thegrowth of these parameters.

B. Evaluating Spatial Keyword Ranking Query

To our best knowledge, CM-CDIR [4] is the state of the arttechnique for the spatial keyword ranking, which is an opti-mized version of IR-tree by applying the clustering technique.We compare the performance of the aggregate IL-Quadtreebased algorithm introduced in Section V-B with IR and CM-CDIR. Fig. 17 reports the performance of three algorithmsagainst the growth of k where Tigers dataset is employed. Theparameter α in Definition 3 is set to 0.3, and other parametersare set to default values. It is shown that aggregate IL-Quadtreetechnique outperformances the IR and CM-CDIR algorithms.

0

4

8

12

16

10 20 30 40 50

Res

pons

e T

ime

(s)

ILQIR

CM-CDIR

(a) Time vs k

0

1k

2k

3k

4k

5k

10 20 30 40 50

# I/

O

ILQIR

CM-CDIR

(b) I/O vs k

Fig. 17. Spatial Keyword Ranking Query

C. Evaluating Direction-Aware TOPK-SK Query

We compare the performance of the direction-awareTOPK-SK query algorithm introduced in Section V-A withDESKS [12], which is the state of the art technique for thisproblem. Fig. 18 illustrates the performance of two algorithmson Cars dataset where the query response time and the numberof I/O accesses are reported as a function of k. The α and βvalues (α < β) of the direction constraint are randomly chosenbetween [0, π

2 ]. It is reported that IL-Quadtree technique canalso efficiently support the direction-aware TOPK-SK query.

0

0.1

0.2

0.3

0.4

0.5

0.6

10 20 30 40 50

Res

pons

e T

ime(

s) ILQ

DESKS

(a) Time vs k

0

50

100

150

200

250

300

10 20 30 40 50

# I/O

ILQDESKS

(b) I/O vs k

Fig. 18. Direction-aware Top k Spatial Keyword Search

VII. CONCLUSIONS

The problem of top k spatial keyword search is importantdue to the increasing amount of spatio-textual objects collectedin a wide spectrum of applications. In the paper, we proposea novel index structure, namely IL-Quadtree, to organize thespatio-textual objects. An efficient algorithm is developedto support the top k spatial keyword search by takingadvantage of the IL-Quadtree. Our comprehensive experimentsconvincingly demonstrate the efficiency of our techniques.

REFERENCES

[1] Y. Zhou, X. Xie, C. Wang, Y. Gong, and W.-Y. Ma, “Hybrid indexstructures for location-based web search,” in CIKM, 2005.

[2] I. D. Felipe, V. Hristidis, and N. Rishe, “Keyword search on spatialdatabases,” in ICDE, 2008.

[3] G. Cong, C. S. Jensen, and D. Wu, “Efficient retrieval of the top-kmost relevant spatial web objects,” PVLDB, vol. 2, no. 1, 2009.

[4] D. Wu, G. Cong, and C. S. Jensen, “A framework for efficient spatialweb object retrieval,” VLDB J., 2012.

[5] R. Hariharan, B. Hore, C. Li, and S. Mehrotra, “Processing spatial-keyword (sk) queries in geographic information retrieval (gir) systems,”in SSDBM, 2007.

[6] D. Wu, M. L. Yiu, G. Cong, and C. S. Jensen, “Joint top k spatialkeyword query processing,” TKDE, 2011.

[7] G. R. Hjaltason and H. Samet, “Distance browsing in spatial databases.”TODS, vol. 24, no. 2, pp. 265–318, 1999.

[8] S. Vaid, C. B. Jones, H. Joho, and M. Sanderson, “Spatio-textualindexing for geographical search on the web,” in SSTD, 2005.

[9] Y.-Y. Chen, T. Suel, and A. Markowetz, “Efficient query processing ingeographic web search engines,” in SIGMOD Conference, 2006.

[10] M. Christoforaki, J. He, C. Dimopoulos, A. Markowetz, and T. Suel,“Text vs. space: efficient geo-search query processing,” in CIKM, 2011.

[11] J. B. Rocha-Junior, O. Gkorgkas, S. Jonassen, and K. Nørvag, “Efficientprocessing of top-k spatial keyword queries,” in SSTD, 2011.

[12] G. Li, J. Feng, and J. Xu, “Desks: Direction-aware spatial keywordsearch,” in ICDE, 2012.

[13] S. B. Roy and K. Chakrabarti, “Location-aware type ahead search onspatial databases: semantics and efficiency,” in SIGMOD Conference,2011.

[14] J. B. Rocha-Junior and K. Nørvag, “Top-k spatial keyword queries onroad networks,” in EDBT, 2012.

[15] A. Khodaei, C. Shahabi, and C. Li, “Hybrid indexing and seamless rank-ing of spatial and textual features of web documents,” in DEXA, 2010.

[16] Z. Li, K. C. K. Lee, B. Zheng, W.-C. Lee, D. L. Lee, and X. Wang,“Ir-tree: An efficient index for geographic document search,” IEEETrans. Knowl. Data Eng., vol. 23, no. 4, 2011.

[17] F. Li, B. Yao, M. Tang, and M. Hadjieleftheriou, “Spatial approximatestring search,” TKDE, 2012.

[18] D. Zhang, Y. M. Chee, A. Mondal, A. K. H. Tung, and M. Kitsuregawa,“Keyword search in spatial databases: Towards searching by document,”in ICDE, 2009.

[19] X. Cao, G. Cong, C. S. Jensen, and B. C. Ooi, “Collective spatialkeyword querying,” in SIGMOD Conference, 2011.

[20] J. Fan, G. Li, L. Zhou, S. Chen, and J. Hu, “Seal: Spatio-textualsimilarity search,” PVLDB, vol. 5, no. 9, 2012.

[21] I. Gargantini, “An effective way to represent quadtrees,” Commun.ACM, vol. 25, no. 12, pp. 905–910, 1982.

[22] G. M. Morton, “A computer oriented geodetic data base and a newtechnique in file sequencing,” Technical Report, Ottawa, Canada: IBMLtd, 1966.

[23] C. Faloutsos, “Multiattribute hashing using gray codes,” in SIGMODConference, 1986.

ACKNOWLEDGMENT Ying Zhang is supported by ARC DP110104880, ARC

DP130103245 and UNSW ECR grant PS27476. Wenjie Zhang is supported by ARC DP120104168 and ARC DE120102144. Xuemin Lin is supported by ARC DP0987557, ARC DP110102937, ARC DP120104168 and NSFC61021004.

912