A note on randomized mutual search
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 (Ir + 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. (C) 1999 Published by Elsevier Science B.V. All rights reserved.
lower bound upper bound two-agent mutual search randomized algorithms algorithms