Www.ntnu.no Efficient Processing of Top-k Spatial Preference Queries João B. Rocha-Junior, Akrivi Vlachou, Christos Doulkeridis, and Kjetil Nørvåg 1 VLDB’

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Efficient Processing of Top-k Spatial Preference Queries

João B. Rocha-Junior, Akrivi Vlachou, Christos Doulkeridis, and Kjetil Nørvåg

1VLDB’ 2011 - Seattle, USA

www.ntnu.no

Outline

• Top-k spatial preference queries• Current approaches• Our approach– Mapping to distance-score space– Query processing– Materialization (index construction)

• Experimental evaluation• Conclusion


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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


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Top-k spatial preference queries


x

bar caféhotel

p1

c4(0.8)

• Returns – Ranked set of k best data objects

• Score of a data object – Obtained from feature objects

in its spatial neighborhood

• Query– Spatial neighborhood– Features of interest (e.g., bars)

c2(0.4)

c1(0.6)

c3(0.2)

b1(0.9)

b3(0.3)

b2(0.6)

p2

p3

y

• Given a set of data objects and scored feature objects

Top-1

Top-1

Top-1

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Score function

• Aggregation of partial scores– 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


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Example (agg=sum)


Range Nearest neighbor Influence

score(p)=1.5 score(p)=1.0 score(p)=0.6

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Current approaches

• Naïve– 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.

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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


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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

9VLDB’2011 - Seattle, USA

x

caféhotel

p1

c5(0.8)c4(0.4)

c2(0.6)

c3(0.2)

y

c1(0.5)

?

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Our framework

• Mapping to distance-score space– 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


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Mapping to the distance-score space

• Mapping– Pairs (object, feature) – Space [distance X score]


p1

c3(0.5)

c1(0.9)

c4(0.3)

c2(0.7)

p2

(p1,c3)

(p1,c4)

(p1,c1)

(p1,c2)

(p2,c1)

(p2,c4)

(p2,c3) (p2,c2)

pair (p2,c)pair (p1,c)caféhotel

• Skyline– Minimize: distance– Maximize: score

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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


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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


Max-heap: <e1(0.8) >root:

e1: e2:

e1 e2

(p3,t4) (p2,t1) (p1,t3) (p3,t4) (p2,t4) (p3,t4)

r=3

Max-heap: <p3(0.8),p2(0.6)>

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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


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1.7+ =

Example (range, r=4.5)

Object R1 R2 Score Upper-bound

r=4.5 r=4.5

R1

p3(0.8) p1(0.9)

R2

hotelX

restaurant

hotelX

restaurant

hotelX

bar

hotelX

bar

p1 - 0.9 0.9 1.7

p3 0.8 - 0.8 1.7


1.2+ =



p3 0.8 - 0.8

p1 - 0.9 0.9

R1

p2(0.6) p2(0.6)

R2

r=4.5 r=4.5

1.4

1.5

p2 0.6 0.6 1.2 1.2


0.5+ =



p3 0.8

p1 0.9

p2 0.6 0.6 1.2 1.2

R1

p1(0.2) p3(0.3)

R2

r=4.5 r=4.5

Top-1 0.2 1.1 1.1

0.3 1.1 1.1

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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


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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.

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Variables studied• Data distribution– 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


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Datasets


DatasetsNumber of

data objectsNumber of

feature objectsDynamic

skyline set

Wal-Mart (WM) 11K 4K 1.98

Hotels (HT) 11K 31K 4.82

Synthetic (CN) 100K 100K 11.26

Uniform (UN) 100K 100K 12.04

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Number of features


a) I/O varying the number of feature sets

b) response time varying thenumber of feature sets

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Scalability


a) response time varying |Fi| b) response time varying |O|

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Real datasets


b) influence c) nearest neighbora) range

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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


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Thanks!

More information:João B. Rocha-Junior

[email protected]://www.idi.ntnu.no/~joao


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Www.ntnu.no Efficient Processing of Top-k Spatial Preference Queries João B. Rocha-Junior, Akrivi Vlachou, Christos Doulkeridis, and Kjetil Nørvåg 1 VLDB’