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.
|Number of pages||5|
|Journal||Information Processing Letters|
|State||Published - 30 Sep 1999|
Bibliographical noteFunding Information:
I Research partially supported by a grant from Israel Ministry of Science and Technology. ∗Corresponding author. Email: firstname.lastname@example.org. 1Email: email@example.com. 2In , a general case of k agents operating in an asynchronous environment is defined too. In this note we focus on the basic synchronous two-agent case, which seems to represent the combinatorial difficulty of the problem.
- Lower bound
- Randomized algorithms
- Two-agent mutual search
- Upper bound