New results on rendezvous search on the interval

Abstract

In a rendezvous search problem, two players are placed in a network and must try to meet each other in the least possible expected time. We look at rendezvous search on a discrete interval in which the players are initially placed using independent draws (usually assumed to be from the same distribution). Some optimal solutions are known if this distribution is uniform, and also for certain other special types of distribution. In this article, we present two new results. First, we characterize the complete set of solutions for the uniform case, showing that all optimal strategies must have two specific properties (namely, of being swept and strictly geodesic). Second, we relate search strategies on the interval to proper binary trees, and use this correspondence to derive a recurrence relation for solutions to the symmetric rendezvous problem for any initial distribution. This relation allows us to solve any such problem computationally by dynamic programming. Finally, some ideas for future research are discussed. © Wiley Periodicals, Inc. Naval Research Logistics 60: 454–467, 2013