### Mutual searchMutual search

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 Author Buhrman, Harry ♦ Franklin, Matthew ♦ Garay, Juan A. ♦ Hoepman, Jaap-Henk ♦ Tromp, John ♦ Vitnyi, Paul Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1999 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Coalition forming ♦ Computational complexity ♦ Computer networks ♦ Datastructures ♦ Discrete algorithms ♦ Distributed computation ♦ Mutual search Abstract We introduce a search problem called “mutual search” where $\textit{k}$ agents, arbitrarily distributed over $\textit{n}$ sites, are required to locate one another by posing queries of the form “Anybody at site $\textit{i}?”.$ We ask for the least number of queries that is necessary and sufficient. For the case of two agents using deterministic protocols, we obtain the following worst-case results: In an oblivious setting (where all pre-planned queries are executed), there is no savings: $\textit{n}™1$ queries are required and are sufficient. In a nonoblivious setting, we can exploit the paradigm of “no news is also news” to obtain significant savings: in the synchronous case $0.586\textit{n}$ queries are required; in the asynchronous case $0.896\textit{n}$ queries suffice and a fortiori $0.536\textit{n}$ queries are required; for on queries and all radomized protocols require at least $0.25\textit{n}$ worst-case expected queries. The graph-theoretic framework we formulate for expressing and analyzing algorithms for this problem may be of independent interest. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1999-07-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 46 Issue Number 4 Page Count 20 Starting Page 517 Ending Page 536

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Source: ACM Digital Library