Preferential top-k search over local data

dissertation thesisRNDr. Martin Šumák

supervisor: doc. RNDr. Stanislav Krajči, PhD.consultant: RNDr. Peter Gurský, PhD.

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Outline

• Top-k search– motivation and example– restrictions and assumptions

• R-tree-based solution– normalization of data– R++-tree

• Grid file-based solution• Experiments– Comparison with B+-trees-based solution, table scan,

etc.2013-08-05 Preferential top-k search over local data, Dissertation thesis, RNDr. Martin Šumák

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Top-k search

• Example– find top 20 apartments with 3 or 4 rooms, not at

first floor, with price about 60000 not exceeding 70000 euro

– moreover, price is the most important attribute and floor is the least important attribute

2013-08-05 Preferential top-k search over local data, Dissertation thesis, RNDr. Martin Šumák

Preferential top-k search over local data - dissertation thesis - Martin Šumák

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Top-k query• k = 20• preferences to attribute’s values – fuzzy functions

• importance of attributes – weights wprice = 3 wrooms = 2 wfloor = 1

2013-08-05

Preferential top-k search over local data - dissertation thesis - Martin Šumák

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Top-k query

• Overall value of object O is3*fprice(Oprice) + 2*frooms(Orooms) + 1*ffloor(Ofloor)

• In general c(fprice(Oprice), frooms(Orooms), ffloor(Ofloor))

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Function c has to be monotone!

Preferential top-k search over local data - dissertation thesis - Martin Šumák

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The goal of top-k search

• to find top-k objects effectively– by processing minimum amount of data

• restrictions and assumptions– all the data is accessible locally– all attributes are numerical

2013-08-05

Preferential top-k search over local data - dissertation thesis - Martin Šumák

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R-tree-based solution• object– a vector of n numbers– a point of n-dimensional space

– R-tree, R*-tree, R+-tree, R++-tree2013-08-05

Preferential top-k search over local data - dissertation thesis - Martin Šumák

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From kNN to top-k search• k nearest neighbour– known incremental algorithm

– distance from “query point Z” is the measure of “closeness”

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Preferential top-k search over local data - dissertation thesis - Martin Šumák

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From kNN to top-k search

• top-k search– overall value (h) is the measure of “goodness”

– by replacing distance with overall value and reversing order we change the result from kNN to top-k

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Preferential top-k search over local data - dissertation thesis - Martin Šumák

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Analogy of kNN and top-k search

• Correctness• Efficiency

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top-k

kNN

Preferential top-k search over local data - dissertation thesis - Martin Šumák

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Disproportion of attribute values

• floor, area, price – very different ranges– solution: normalization – linear transformation of

attribute values to interval [0; 1]

• Another disproportion comes from weights2013-08-05

Preferential top-k search over local data - dissertation thesis - Martin Šumák

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Normalization applicability

• Useful for– R*-tree

• Meaningless for– R-tree (proven for the quadratic split method)– R+-tree, R++-tree– Grid file

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Preferential top-k search over local data - dissertation thesis - Martin Šumák

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Why the R++-tree• Zero overlaps & minimum

bounding rectangles may cause a problem when adding new object

• R+-tree avoids overlaps at the price of rectangles size

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Preferential top-k search over local data - dissertation thesis - Martin Šumák

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The R++-tree idea

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• Zero overlaps & minimum bounding rectangles may cause a problem when adding new object

• R++-tree keeps two rectangles for each node – the minimum one and the parent covering one

Preferential top-k search over local data - dissertation thesis - Martin Šumák

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The R++-tree properties

• Height-balanced• Zero overlaps• Overflow nodes at leaf level only• Minimum node occupancy is 1

• For the top-k search purposes, attribute values can be strings or any other comparable values (not just numbers)

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Preferential top-k search over local data - dissertation thesis - Martin Šumák

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Top-k search over Grid file

• Grid file is a spatial index for point data• We used static Grid file without extra directory

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Preferential top-k search over local data - dissertation thesis - Martin Šumák

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Top-k search over Grid file

• We have proven correctness and efficiency as well

2013-08-05