Group 8: Denial Hess, Yun Zhang

Project presentation

MessagesWhat :Get near real-time K nearest neighbor (KNN) query responses in spatial networks, while minimizing the storage cost

How: 1) Calculate shortest path: Dijkstra-based approach Pre-compute –based approach2) Search query objects:

Blind search Hierarchical algorithm to skip regions where no query object type is contained

Evidence: location-based service

Agenda Motivation Notation Problem Statement Related Work Proposed Solution Validation Summary

Motivation Popularity of query in spatial networks

Online map serviceMobile serviceKNN query is basic and widely used

Existing approach

Can work out KNN query answer But, for typical spatial network (100,000 nodes, 100,000

edges)-> expensive computational cost or storage cost

Therefore: Need more effective algorithm!

Notation (1/2)Graph G= (N, E, C): a directed flat graph consisting of a

node set N, a cost set C, and an edge set E.Fragment: a sub-graph of G, which consists a subset of

nodes and edges of G.Boundary node (BN): a node that has neighbors in more

than one fragment.Hierarchical graph: a 2-level representation of the

original graph.

The lower-level is composed of a set of disjoint fragments The higher-level is comprised of the boundary nodes

Notation (2/2)Materialization:

Full: all relevant information pre-computed and stored.

Virtual: no information pre-stored.

Hybrid: some relevant information pre-stored, some left for real-time computation.

Problem StatementResearch question: how can we get a near real time response to KNN query in a spatial network, while minimizing the storage cost?

Given: Graph G, a query node q, a required number of nearest neighbors k.

Output: k nearest neighbors of query node q.Objective: near real time query response,

minimize storage costConstraint: output is correct. Computation is

based on spatial network. Spatial network is static.

Related WorkSolution-based approach (store distances

between all pairs of nodes) limitation: storage costDijkstra-based approach (Dijkstra algorithm) limitation: computational costPre-compute-based approach (reduce search

regions) limitation: storage costPre-knowledge-based approach (assume query

object type is known in advance) limitation: assumption is not practical

Proposed Solution1) To speed up shortest path calculation

Pre-compute 2) To avoid blind search in spatial networks

Hierarchical algorithm to skip regions where no query objects are contained

ChallengesNeed to decide a proper degree of

materializationNeed to deal with situations like:

Large spatial network data; Query node is moving;

These situations cause computational and storage challenges.

Working Stepsa) Use CCAM to represent spatial network

(involve graph partition, build hierarchy)b) Pre-compute and store shortest path

informationc) Use ‘Incremental Network Expansion’

framework; Use pre-compute results to calculate shortest paths ;Use hierarchy to skip regions;

Solution Example (1/2)

Spatial Network GraphNode = object,Edge = Street

Digital number=distanceyellow node=query node

Figure 1: Shortest path calculation

Solution Example (2/2)

qqn1

n2n2

n3n3

n5

n4n4

n7

n6n6

Figure 2: Skip regions which contain no query object type

Validation (1/3)Comparison of materialization

SPC-B: store shortest path cost between boundary nodes;SPC-B,IB: store shortest path cost between boundary nodes and shortest path cost between interior nodes and boundary nodes;

Test Data : A real road network CA(10,000 nodes, 10,215 edges)

Validation (2/3) Performance Measure

Storage Size;Execution Time;

Validation (3/3)Approach Storage Cost

Complexity

IER O(N)

INE O(N)

Shortest Path Quadtree

H-KNN

O(N^1.5)

O(N^1.33)

N is the total nodes of a spatial network

Moving Object

a

b

e

f

c

d

qq

q is a moving object

Shortest path cost from q to c:Min{ |qa|+|ac|, |qb|+|bc|}

Network Update

a

b c d

Edge value |bc| increaseOriginal shortest path from a to d: a b c d

Store shortest path information:Address network update:1)Detect affected shortest paths2)Update shortest paths, shortest paths cost

Edge value |bc| decreaseOriginal shortest path from a to d: a d

SummaryContribution: Get near real-time K nearest neighbor (KNN) query responses in spatial networks, while minimizing the storage costNovelty: 1) Speed up shortest path calculation: Pre-compute –based approach2) Speed up query objects search:

Hierarchical algorithmFuture Work:More study on dynamic networkCompare with other state-of-the-art approaches

QuestionHow to deal with dynamic network is a challenge.

There are network change situations like edge value change,

what are other possible network changes? How would you

like to deal with the dynamic network?