Randomised Mutual Search for k > 2 Agents

Abstract

We study the efficiency of randomised solutions to the mutual search problem of finding k agents distributed over n nodes. For a restricted class of so-called linear randomised mutual search algorithms we derive a lower bound of $\frac{{k - 1}} {{k + 1}}\left( {n + 1} \right)$ (n + 1) expected calls in the worst case. A randomised algorithm in the shared-coins model matching this bound is also presented. Finally we show that in general more adaptive randomised mutual algorithms perform better than the lower bound for the restricted case, even when given only private coins. A lower bound for this case is also derived.

Id: rnd-mutsearch.tex,v 1.15 2001/06/25 13:27:01 hoepman Exp