S CALABLE S KYLINE C OMPUTATION U SING O BJECT - BASED S PACE P ARTITIONING Shiming Zhang Nikos Mamoulis David W. Cheung sigmod

O UTLINE Introduction Object-based Space Partitioning Recursive Object-based Space Partitioning Left-Child/Right-Sibling Skyline Tree OSPSOnSortingFirst OSPSOnPartitioningFirst FilterDominatedPartitions Experimental Results Conclusions 2

I NTRODUCTION (1) Skyline queries are useful in multi-criteria decision making applications that involve high dimensional and large datasets. There is a number of methods that operate on pre-computed indexes on the data. Compare each accessed point with the skyline points found so far. 3

I NTRODUCTION (2) 4

N OTATION 5

O BJECT - BASED S PACE P ARTITIONING reference skyline 6

R ECURSIVE O BJECT - BASED S PACE P ARTITIONING reference skyline 7

W HY CAN SAFELY SKIP ?  Skip all incomparable partitions according to Corollary 1 8

L EFT -C HILD /R IGHT -S IBLING S KYLINE T REE 9

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LCRS T REE G ROWTH 11

T RACE 12

OSP S KYLINE A LGORITHMS 1 13

OSP S KYLINE A LGORITHMS 2 14

OSP S KYLINE A LGORITHMS 15

OSP S KYLINE A LGORITHMS 16

E XPERIMENTAL E VALUATION Three types of synthetic datasets anti-correlated (AC) NBA uniform and independent (UI) Household correlated (CO) Color 17

E XPERIMENTAL R ESULTS 18

E XPERIMENTAL R ESULTS 19

C ONCLUSIONS Proposed an efficient set of skyline evaluation algorithms that are based on the idea of organizing the discovered skyline points in a tree. Each candidate skyline object only needs to be compared for dominance with a small subset of the existing skyline points. (skip incomparable sets ) Makes our solutions scalable to the dimensionality, a feature that all previously proposed skyline algorithms lack. 20