Mutual Search
Abstract
We introduce a search problem called ``mutual search'' where $k$ \agents, arbitrarily distributed over $n$ sites, are required to locate one another by posing queries of the form ``Anybody at site $i$?''. 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 worstcase results: In an oblivious setting (where all preplanned queries are executed) there is no savings: $n1$ 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 $0.586n$ queries suffice and $0.536n$ queries are required; in the asynchronous case $0.896n$ queries suffice and a fortiori 0.536 queries are required; for $o(\sqrt{n})$ \agents using a deterministic protocol less than $n$ queries suffice; there is a simple randomized protocol for two \agents with worstcase expected $0.5n$ queries and all randomized protocols require at least $0.125n$ worstcase expected queries. The graphtheoretic framework we formulate for expressing and analyzing algorithms for this problem may be of independent interest.
 Publication:

arXiv eprints
 Pub Date:
 February 1999
 arXiv:
 arXiv:cs/9902005
 Bibcode:
 1999cs........2005B
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Complexity;
 Computer Science  Databases;
 Computer Science  Distributed;
 Parallel;
 and Cluster Computing;
 Computer Science  Discrete Mathematics;
 Computer Science  Information Retrieval;
 F.2;
 C.2;
 E;
 1;
 D.4.4
 EPrint:
 18 pages, Latex, 5 figures, J. Assoc. Comp. Mach., To appear