TY - JOUR

T1 - A note on randomized mutual search

AU - Lotker, Zvi

AU - Patt-Shamir, Boaz

N1 - Funding Information:
I Research partially supported by a grant from Israel Ministry of Science and Technology. ∗Corresponding author. Email: [email protected]. 1Email: [email protected]. 2In [1], 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.

PY - 1999/9/30

Y1 - 1999/9/30

N2 - 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.

AB - 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.

KW - Algorithms

KW - Lower bound

KW - Randomized algorithms

KW - Two-agent mutual search

KW - Upper bound

UR - http://www.scopus.com/inward/record.url?scp=0032621024&partnerID=8YFLogxK

U2 - 10.1016/s0020-0190(99)00112-x

DO - 10.1016/s0020-0190(99)00112-x

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AN - SCOPUS:0032621024

SN - 0020-0190

VL - 71

SP - 187

EP - 191

JO - Information Processing Letters

JF - Information Processing Letters

IS - 5-6

ER -