Skyline Computation with Noisy Comparisons

TL;DR

This paper presents new output-sensitive algorithms for computing the skyline in noisy comparison models, significantly improving query complexity bounds and providing tight results in low dimensions.

Contribution

It introduces two novel algorithms with improved query complexities for skyline computation under noisy comparisons, advancing prior bounds in the field.

Findings

Algorithms achieve query complexities of O(nd log(dk/δ)) and O(ndk log(k/δ)).

Results are tight bounds for low-dimensional cases.

Enhances skyline computation efficiency in noisy, crowdsourcing scenarios.

Abstract

Given a set of $n$ points in a $d$-dimensional space, we seek to compute the skyline, i.e., those points that are not strictly dominated by any other point, using few comparisons between elements. We adopt the noisy comparison model [FRPU94] where comparisons fail with constant probability and confidence can be increased through independent repetitions of a comparison. In this model motivated by Crowdsourcing applications, Groz & Milo [GM15] show three bounds on the query complexity for the skyline problem. We improve significantly on that state of the art and provide two output-sensitive algorithms computing the skyline with respective query complexity $O(nd\log (dk/\delta))$ and $O(ndk\log (k/\delta))$ where $k$ is the size of the skyline and $\delta$ the expected probability that our algorithm fails to return the correct answer. These results are tight for low dimensions.