Rendezvous Search in a Graph

Abstract

The rendezvous search problem in a graph has been widely studied. The problem is defined as follows: two players are initially placed randomly in a space $\mathscr {S}$ which can be represented by discrete points or is continuous. Two players want to meet up, which is the so-called “rendezvous”. In a compact space, it is hard to define how exactly two players meet. Therefore, we assume they are said to meet if their distance is no larger than a given value r. This assumption is reasonable because two players can look around and find each other if someone is within the field of vision. r can be considered the detection radius of the player. The goal of rendezvous search is to minimize the time for the players to meet. In this chapter, we first introduce the hardness of rendezvous search in Sect. 18.1, where two types of symmetry are presented. In order to show the intuitive ideas of designing rendezvous search algorithms, we choose rendezvous search along a cycle as the example in Sect. 18.2. The rendezvous search algorithms are presented in Sect. 18.3, and we summarize the chapter in Sect. 18.4.