Post on 02-Jan-2016
Handling Spatial Data In P2P Systems
Verena Kantere, Timos Sellis, Yannis Kouvaras
Problem Definition
Assumptions: Structure P2P Overlays Spatial Data in Peers
Problem: Necessity for indexing and routing
techniques for such an environment
Technique Requirements
We need a technique that: Guarantees the retrieval of any existing
spatial information in the system Achieves satisfying index size for any node Achieves a satisfying length for any search
path Provides easier access to popular
information Preserves proximity of areas
Related Work
P2PR-tree (Workshop of EDBT ‘04) Quad-tree approach (Poster in
ICDE’05) kd-tree approach (WebDB’04)
Partitioning Space
Spatial Coding
0
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1
2
2
2
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3
3
3
4
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4
5
5 6
0
1
1
2
2
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3
4
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5 6
1
1
02
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2
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3
3
3
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56
Partitioning Space cont’d
The code of an area A is: A azaxay
az: is the granularity level, i.e. the size in terms of cells. ax: is the average of the digit d1 of all the area cells. ay: is the average of the digit d2 of all the area cells.
Distance Metrics:d1(A1, A2) = |a1x-a2x|+|a1y-a2y|d2(A1, A2) = ||a1x-a2x|-|a1y-a2y||
D(A1, A2) d1d2
Dzoom(A1, A2) D(A1, A2)/(0.5*|A1.az+A2.az|)
Distributed Indexing for Spatial Areas
Distributed Indexing Algorithm Step 1: Indexing the grids of each level Phase A: Indexing areas of the same
grid Phase B: Indexing areas of other grids of
the same level Step 2: Indexing the grids of other
levels
Grid Example
0 7 1 6
1 8 3 6
5 6
7 6
9 6
11 6
13 6
3 8
5 8
7 8
9 8
11 8
13 8
2 7
4 7
6 7
8 7
10 7
12 7
14 7
3 4
5 4
7 4
9 4
11 4
2 5
4 5
6 5
8 5
10 5
12 5
5 2
7 2
9 2
4 3
6 3
8 3
10 3
6 1
8 1
7 0
3 10
5 10
7 10
9 10
11 10
5 12
7 12
9 12
2 9
4 9
6 9
8 9
10 9
12 9
4 11
6 11
8 11
10 11
6 13
8 137 14
Direct Neighbors &Data Hashing
Peers have 2 neighbors on each dimension: Horizontal Vertical PerpendicularNeighbors are the closest peers on each
direction. Areas are stored to the closest neighbor
following a priorities of dimensions
Direct Neighbors: Examples
horizontal successor
verticalsuccessor
horizontalpredecessor
verticalpredecessor
1st quadrant2nd quadrant
3rd quadrant 4th quadrant
Routing of Spatial Queries
Basic Routing Algorithm Step 1: Find a peer corresponding to
the same size as the sought area. Step 2: Find a peer hosting the sought
area or an overlapping area of the latterStep 3: Find the peer hosting the sought
area
Routing Example
0 7 1 6
1 8 3 6
5 6
7 6
9 6
11 6
13 6
3 8
5 8
7 8
9 8
11 8
13 8
2 7
4 7
6 7
8 7
10 7
12 7
14 7
3 4
5 4
7 4
9 4
11 4
2 5
4 5
6 5
8 5
10 5
12 5
5 2
7 2
9 2
4 3
6 3
8 3
10 3
6 1
8 1
7 0
3 10
5 10
7 10
9 10
11 10
5 12
7 12
9 127 14
2 9
4 9
6 9
8 9
10 9
12 9
4 11
6 11
8 11
10 11
6 13
8 13
1
2
suc
suc
su
c
suc
suc/pred
3
pred
Details…
0 7 1 6
1 8 3 6
5 6
7 6
9 6
11 6
13 6
3 8
5 8
7 8
9 8
11 8
13 8
2 7
4 7
6 7
8 7
10 7
12 7
14 7
3 4
5 4
7 4
9 4
11 4
2 5
4 5
6 5
8 5
10 5
12 5
5 2
7 2
9 2
4 3
6 3
8 3
10 3
6 1
8 1
7 0
3 10
5 10
7 10
9 10
11 10
5 12
7 12
9 12
2 9
4 9
6 9
8 9
10 9
12 9
4 11
6 11
8 11
10 11
6 13
8 137 14
suc
suc
0 7 1 6
1 8 3 6
5 6
7 6
9 6
11 6
13 6
3 8
5 8
7 8
9 8
11 8
13 8
2 7
4 7
6 7
8 7
10 7
12 7
14 7
3 4
5 4
7 4
9 4
11 4
2 5
4 5
6 5
8 5
10 5
12 5
5 2
7 2
9 2
4 3
6 3
8 3
10 3
6 1
8 1
7 0
3 10
5 10
7 10
9 10
11 10
5 12
7 12
9 12
2 9
4 9
6 9
8 9
10 9
12 9
4 11
6 11
8 11
10 11
6 13
8 13
-2 7 -1 6
-1 8
0 5 1 4 2 3 3 2 4 1 5 0 6 -1 7 -2
0 9
1 10
2 11
3 12
4 13
5 14
6 15
7 16
8 -1
9 0
10 1
11 2
12 3
13 4
14 5
15 6
16 78 15 9 14 10 13 11 12 12 11 13 10 14 9 15 8
7 14
Complexity Characteristics
Complexity for both pure Chord and our method is O(3log2n).
But with our method: Peers with big areas are favored with
small indexes Shorter search paths for bigger areas The search path grows with the
relative distance
Assignment of Peer IDs
The peer ID plays a significant role in our approach joining peers can ask for specific ids: it is adequate to assign an id that
belongs to the same or similar level as the requested id
The above constraint loosens with the size of the area (higher levels are more connected)
Preliminary Experiments
0
1
2
3
4
5
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6> 12> 24> RANDProximity
Ave
rage
# o
f hop
s
S1024 C1024 S2048 C2048 S4096 C4096
Preliminary Experiments (2)
0
1
2
3
4
5
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6> 12> 24> RANDProximity
Ave
rage
# o
f hop
s
S400 C400 S900 C900 S1400 C1400