An optimal randomised cell probe lower bound for approximate nearest neighbour searching

Amit Chakrabarti, Oded Regev

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

Abstract

We consider the approximate nearest neighbour search problem on the Hamming Cube {0, 1}d. We show that a randomised cell probe algorithm that uses polynomial storage and word size do(1) requires a worst case query time of Ω (log log d/ log log log d). The approximation factor may be as loose as 2log1-ηd for any fixed η > 0. This generalises an earlier result [5] on the deterministic complexity of the same problem and, more importantly, fills a major gap in the study of this problem since all earlier lower bounds either did not allow randomisation [5, 18] or did not allow approximation [4, 2, 15]. We also give a cell probe algorithm which proves that our lower bound is optimal. Our proof uses a lower bound on the round complexity of the related communication problem. We show, additionally, that considerations of bit complexity alone cannot prove any nontrivial cell probe lower bound for the problem. This shows that the Richness Technique [20] used in a lot of recent research around this problem would not have helped here. Our proof is based on information theoretic techniques for communication complexity, a theme that has been prominent in recent research [6, 1, 23, 14]. In particular, we make heavy use of the round elimination and message compression ideas in the recent work of Sen [23] and Jain, Radhakrishnan, and Sen [14], and also introduce a new technique which we call message switching.

Original languageEnglish (US)
Title of host publicationProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Pages473-482
Number of pages10
StatePublished - 2004
EventProceedings - 45th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2004 - Rome, Italy
Duration: Oct 17 2004Oct 19 2004

Other

OtherProceedings - 45th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2004
CountryItaly
CityRome
Period10/17/0410/19/04

ASJC Scopus subject areas

  • Engineering(all)

Fingerprint Dive into the research topics of 'An optimal randomised cell probe lower bound for approximate nearest neighbour searching'. Together they form a unique fingerprint.

  • Cite this

    Chakrabarti, A., & Regev, O. (2004). An optimal randomised cell probe lower bound for approximate nearest neighbour searching. In Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS (pp. 473-482)