Randomized algorithms for comparison-based search

Dominique Tschopp, Suhas Diggavi, Payam Delgosha, Soheil Mohajer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Scopus citations

Abstract

This paper addresses the problem of finding the nearest neighbor (or one of the R-nearest neighbors) of a query object q in a database of n objects, when we can only use a comparison oracle. The comparison oracle, given two reference objects and a query object, returns the reference object most similar to the query object. The main problem we study is how to search the database for the nearest neighbor (NN) of a query, while minimizing the questions. The difficulty of this problem depends on properties of the underlying database. We show the importance of a characterization: combinatorial disorder D which defines approximate triangle inequalities on ranks. We present a lower bound of Ω(Dlog n/D + D 2) average number of questions in the search phase for any randomized algorithm, which demonstrates the fundamental role of D for worst case behavior. We develop a randomized scheme for NN retrieval in O(D 3 log 2 n + Dlog 2 n log log n D3 ) questions. The learning requires asking O(nD 3 log 2 n + Dlog 2 n log log n D3 ) questions and O(n log 2 n/ log(2D)) bits to store.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 24
Subtitle of host publication25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011
StatePublished - Dec 1 2011
Event25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011 - Granada, Spain
Duration: Dec 12 2011Dec 14 2011

Publication series

NameAdvances in Neural Information Processing Systems 24: 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011

Other

Other25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011
CountrySpain
CityGranada
Period12/12/1112/14/11

Cite this