A note on randomized mutual search

Zvi Lotker, Boaz Patt-Shamir

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In Mutual Search, recently introduced by Buhrman et al. (1998), static agents are searching for each other: each agent is assigned one of n locations, and the computations proceed by agents sending queries from their location to other locations, until one of the queries arrives at the other agent. The cost of a search is the number of queries made. The best known bounds for randomized protocols using private coins are (1) a protocol with worst-case expected cost of [(n + 1)/2], and (2) a lower bound of (n - 1)/8 queries for randomized protocols which make only a bounded number of coin-tosses. In this paper we strictly improve the lower bound, and present a new upper bound for shared random coins. Specifically, we first prove that the worst-case expected cost of any randomized protocol for two-agent mutual search is at least (n + 1)/3. This is an improvement both in terms of number of queries and in terms of applicability. We also give a randomized algorithm for mutual search with worst-case expected cost of (n + 1)/3. This algorithm works under the assumption that the agents share a random bit string. This bound shows that no better lower bound can be obtained using our technique.

Original languageEnglish
Pages (from-to)187-191
Number of pages5
JournalInformation Processing Letters
Volume71
Issue number5-6
DOIs
StatePublished - 30 Sep 1999
Externally publishedYes

Bibliographical note

Funding Information:
I Research partially supported by a grant from Israel Ministry of Science and Technology. ∗Corresponding author. Email: zvilo@eng.tau.ac.il. 1Email: boaz@eng.tau.ac.il. 2In [1], a general case of k agents operating in an asynchronous environment is defined too. In this note we focus on the basic synchronous two-agent case, which seems to represent the combinatorial difficulty of the problem.

Keywords

  • Algorithms
  • Lower bound
  • Randomized algorithms
  • Two-agent mutual search
  • Upper bound

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