A note on randomized mutual search

Zvi Lotker*, Boaz Patt-Shamir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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
Issue number5-6
StatePublished - 30 Sep 1999


FundersFunder number
Ministry of Science and Technology, Israel


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


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