Cell-probe lower bounds for the partial match problem

T. S. Jayram, Subhash Khot, Ravi Kumar, Yuval Rabani

Research output: Contribution to journalArticlepeer-review

Abstract

Given a database of n points in {0,1}d, the partial match problem is: In response to a query x in {0,1,*}d, is there a database point y such that for every i whenever xi≠*, we have xi = yi. In this paper we show randomized lower bounds in the cell-probe model for this well-studied problem (Analysis of associative retrieval algorithms, Ph.D. Thesis, Stanford University, 1974; The Art of Computer Programming; Sorting and Searching, Addison-Wesley, Reading, MA, 1973; SIAM J. Comput. 5(1) (1976) 19; J. Comput. System Sci. 57(1) (1998) 37; Proceedings of the 31st Annual ACM Symposium on Theory of Computing, 1999; Proceedings of the 29th International Colloquium on Algorithms, Logic, and Programming, 1999). Our lower bounds follow from a near-optimal asymmetric communication complexity lower bound for this problem. Specifically, we show that either Alice has to send Ω(d/logn) bits or Bob has to send Ω(n1-o(1)) bits. When applied to the cell-probe model, it means that if the number of cells is restricted to be poly(n,d) where each cell is of size poly(logn,d), then Ω(d/log2n) probes are needed. This is an exponential improvement over the previously known lower bounds for this problem obtained by Miltersen et al. (1998) and Borodin et al. (1999). Our lower bound also leads to new and improved lower bounds for related problems including a lower bound for the ℓ c-nearest neighbor problem for c<3 and an improved communication complexity lower bound for the exact nearest neighbor problem.

Original languageEnglish (US)
Pages (from-to)435-447
Number of pages13
JournalJournal of Computer and System Sciences
Volume69
Issue number3 SPEC. ISS.
DOIs
StatePublished - Nov 2004

Keywords

  • Asymmetric communication complexity
  • Cell-probe model
  • Nearest neighbor problem
  • Partial match problem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics

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