Deterministic rendezvous in restricted graphs

Abstract

In this paper we consider the problem of synchronous rendezvous in which two anonymous mobile entities (robots) A and B are expected to meet at the same time and point in a graph G = (V,E). Most of the work devoted to rendezvous in graphs assumes that robots have access to the same sets of nodes and edges, where the topology of connections may be initially known or unknown. In our work we assume the movement of robots is restricted by the topological properties of the graph space coupled with the intrinsic characteristics of robots preventing them from visiting certain edges in E. We consider three rendezvous models reflecting on restricted maneuverability of robots A and B. In Edge Monotonic Model each robot X ∈ {A,B} has weight wX and each edge in E has a weight restriction. Consequently, a robot X is only allowed to traverse edges with weight restrictions greater that wX. In the remaining two models graph G is unweighted and the restrictions refer to more arbitrary subsets of traversable nodes and edges. In particular, in Node Inclusive Model the set of nodes VX available to robot X, for X ∈ {A,B} satisfies the condition VA ⊆ VB or vice versa, and in Blind Rendezvous Model the relation between VA and VB is arbitrary. In each model we design and analyze efficient rendezvous algorithms. We conclude with a short discussion on the asynchronous case and related open problems.