1. Efficient Processing of Top-k Spatial Preference Queries
João B. Rocha-Junior, Akrivi Vlachou, Christos Doulkeridis, and Kjetil Nørvåg
VLDB’ Seattle, USA

2. Outline Top-k spatial preference queries Current approaches
Our approach
Mapping to distance-score space
Query processing
Materialization (index construction)
Experimental evaluation
Conclusion
VLDB’ Seattle, USA

3. Motivation
Increasing number of Web information systems specialized in location-based queries
Systems are limited to simple spatial queries
Example: return objects in a given spatial location
Top-k spatial preference query
Ranks data objects based on the score of feature objects in their spatial neighborhood
Combines spatial and non-spatial scores
Limited to queries restricted to spatial constraints
This query take in account the quality (score) of the features
VLDB’ Seattle, USA

4. Top-k spatial preference queries
Given a set of data objects and scored feature objects
hotel
bar
café y
b1(0.9)
b3(0.3)
b2(0.6)
Query
Spatial neighborhood
Features of interest (e.g., bars)
c1(0.6)
Top-1 p2
Returns
Ranked set of k best data objects p1
Top-1
c2(0.4)
Score of a data object
Obtained from feature objects in its spatial neighborhood
c4(0.8)
c3(0.2) p3
Top-1 x
VLDB’ Seattle, USA

5. Score function Aggregation of partial scores Partial score
Any monotone function: sum, max, and min
Partial score
Score of a data object for a set of feature objects
Defined by the score of a single feature object
Highest score
Satisfies the spatial constraint
Spatial constraint
Range, nearest neighbor, and influence
VLDB’ Seattle, USA

6. Example (agg=sum) score(p)=1.5 score(p)=1.0 score(p)=0.6 Range
Nearest neighbor
Influence
score(p)=1.5
score(p)=1.0
score(p)=0.6
VLDB’ Seattle, USA

7. Current approaches Naïve State-of-the-art [1,2]
Compute the score of all objects, select the top-k
Very costly
State-of-the-art [1,2]
Data objects and feature objects are indexed by multi-dimensional indices
[1] Yiu, M.L., Dai, X., Mamoulis, N., Vaitis, M., : “Top-k spatial preference queries”, ICDE, 2007.
[2] Yiu, M.L., Lu, H., Mamoulis, N., Vaitis, M.: “Ranking spatial data by quality preferences”, TKDE, 2011.
VLDB’ Seattle, USA

8. Current approaches Probing algorithms (SP and GP)
Requires computing the score for all objects
Branch and bound algorithms (BB and BB*)
Compute an upper-bound score for the entries in the data objects R-tree
Prune entries whose upper-bound score is smaller than the score of the k-th object found
Feature join algorithm (FJ)
Create combinations of feature sets with high score
Combinations whose score is smaller than the score of the k-th object found are pruned
VLDB’ Seattle, USA

9. Motivation behind our idea…
Few feature objects are necessary to compute the score of a data object
Features not dominated by any other feature in terms of both distance and score
Nice properties
Small size in practice
Sufficient to support any neighborhood condition and query parameter y
c1(0.5)
c2(0.6) p1 ?
c4(0.4)
c5(0.8)
c3(0.2)
Make dominate clear x
hotel
café
VLDB’ Seattle, USA

10. Our framework Mapping to distance-score space Identify SKY(p, Fi)
Pairs of objects (p, t) with t  Fi to be examined
Identify SKY(p, Fi)
Minimum set of pairs required to compute the score of p according to Fi for any query
Materialize SKY(p, Fi)
Stored in a R-tree, one R-tree Ri per feature set Fi
Efficient query processing and maintenance
Query processing algorithm
VLDB’ Seattle, USA

11. Mapping to the distance-score space
pair (p2,c)
pair (p1,c)
café
hotel
(p2,c1)
(p1,c1) p1
c3(0.5)
c1(0.9)
c4(0.3)
c2(0.7) p2
(p1,c2)
(p2,c3)
(p2,c2)
(p1,c3)
(p2,c4)
(p1,c4)
Mapping
Pairs (object, feature)
Space [distance X score]
Skyline
Minimize: distance
Maximize: score
VLDB’ Seattle, USA

12. Theoretical properties
SKY(p, Fi) is sufficient to determine the partial score of p for any spatial preference query
Maintaining SKY(p, Fi) is sufficient to answer any spatial preference query (stored in an R-tree)
SKY(p, Fi) is the minimum set required
The data required to process range queries permits processing nn and influence queries
The proofs of the theorems can be found in the paper
VLDB’ Seattle, USA

13. Access to partial scores
Only node entries that satisfy the spatial constraint are accessed
Items are retrieved in decreasing order of score
Minor modifications to support nn and influence
root: e1 e2
Max-heap: <p3(0.8),p2(0.6)>
Max-heap: <e1(0.8) >
e1:
(p3,t4)
(p2,t1)
(p1,t3)
e2:
(p3,t4)
(p2,t4)
(p3,t4)
VLDB’ Seattle, USA

14. Query processing
Compute top-k data objects progressively aggregating partial scores retrieved from Ri
Similar to Fagin’s algorithm (NRA)
Algorithm
Each time an object p is retrieved from Ri, any unseen object p’ in Ri has a score(p’) ≤ score(p)
Keep track of lower and upper-bound score of the seen objects
Terminates when the lower-bound of the k-th object is better than the upper-bound of the remaining objects
VLDB’ Seattle, USA

15. Example (range, r=4.5) + R1 p3(0.8) p1(0.9) R2 = 1.7 r=4.5 r=4.5 hotel
restaurant
bar R1
p3(0.8)
p1(0.9) R2 + =
1.7
Object R1 R2
Score
Upper-bound p3
0.8 -
1.7 p1 -
0.9
1.7
VLDB’ Seattle, USA

16. Example (range, r=4.5) + R1 p2(0.6) R2 = 1.2 r=4.5 r=4.5 Object R1 R2
Score
Upper-bound p3
0.8 - p1
0.9
1.4
1.5 p2
0.6
1.2
VLDB’ Seattle, USA

17. Example (range, r=4.5) + R1 p1(0.2) p3(0.3) R2 = 0.5 Top-1 r=4.5 r=4.5
Object R1 R2
Score
Upper-bound p3
0.8 p1
0.9 p2
0.6
1.2
0.3
1.1
Top-1
0.2
1.1
VLDB’ Seattle, USA

18. Materialization Objects are partitioned into regions
The distance among objects in the same region is small
The skyline set of the objects in the same region is similar with high probability
Compute SKY(R, Fi) for the region R
SKY(p, Fi)  SKY(R, Fi), ∀p  R
Advantage
The feature set is accessed only once to compute the dynamic skyline of all objects in the region
Should I explain dynamic skyline?
VLDB’ Seattle, USA

19. Experimental evaluation
We compare our approach (SFA) against SP, GP, BB, BB*, and FJ algorithms [1,2]
All approaches are implemented in Java
Measures: response time, I/O, update time, index construction time, and index size
[1] Yiu, M.L., Dai, X., Mamoulis, N., Vaitis, M., : “Top-k spatial preference queries”, ICDE, 2007.
[2] Yiu, M.L., Lu, H., Mamoulis, N., Vaitis, M.: “Ranking spatial data by quality preferences”, TKDE, 2011.
VLDB’ Seattle, USA

20. Variables studied Data distribution Cardinality (object and features)
Uniform (UN), Synthetic (CN), Real (RL)
Cardinality (object and features)
50K, 100K, 200K, 400K, 800K, 1600K
Number of results (k)
10, 20, 30, 40, 50
Number of feature sets
1, 2, 3, 4 5
Query range (r), for range and influence queries
10, 40, 160, 640, 2560
VLDB’ Seattle, USA

21. Number of feature objects
Datasets
Datasets
Number of data objects
Number of feature objects
Dynamic skyline set
Wal-Mart (WM)
11K 4K
1.98
Hotels (HT)
31K
4.82
Synthetic (CN)
100K
11.26
Uniform (UN)
12.04
VLDB’ Seattle, USA

22. Number of features a) I/O varying the number of feature sets
b) response time varying the
number of feature sets
VLDB’ Seattle, USA

23. Scalability b) response time varying |O| a) response time varying |Fi|
VLDB’ Seattle, USA

24. Real datasets a) range b) influence c) nearest neighbor
VLDB’ Seattle, USA

25. Conclusion
Top-k spatial preference queries are a useful tool for novel location-based applications
We propose a new approach for processing top-k spatial preference queries efficiently
We find and materialize SKY(p, Fi)
We prove that SKY(p, Fi) is sufficient to determine the partial score of p for any spatial preference query
The size of SKY(p, Fi) is small in practice
We propose algorithms to process queries using our index
The efficiency of our approach is verified through experiments on synthetic and real datasets
VLDB’ Seattle, USA

26. Thanks!
More information: João B. Rocha-Junior
VLDB’ Seattle, USA