Rendezvous of Distance-aware Mobile Agents in Unknown Graphs
Shantanu Das (LIF), Dariusz Dereniowski, Adrian Kosowski (INRIA, Rocquencourt, LIAFA), Przemyslaw Uznanski (LIF)

TL;DR
This paper introduces distance-aware mobile agents that can measure their distance to each other, enabling rendezvous in unknown graphs within polynomial time based on local parameters, improving over previous exponential bounds.
Contribution
The paper presents a novel rendezvous algorithm for distance-aware agents in unknown graphs with polynomial time complexity, along with matching lower bounds.
Findings
Rendezvous can be achieved in polynomial time with distance-awareness.
The algorithm's time complexity is $O(\Delta(D+\log l))$.
Lower bounds show near-optimality of the proposed algorithm.
Abstract
We study the problem of rendezvous of two mobile agents starting at distinct locations in an unknown graph. The agents have distinct labels and walk in synchronous steps. However the graph is unlabelled and the agents have no means of marking the nodes of the graph and cannot communicate with or see each other until they meet at a node. When the graph is very large we want the time to rendezvous to be independent of the graph size and to depend only on the initial distance between the agents and some local parameters such as the degree of the vertices, and the size of the agent's label. It is well known that even for simple graphs of degree , the rendezvous time can be exponential in in the worst case. In this paper, we introduce a new version of the rendezvous problem where the agents are equipped with a device that measures its distance to the other agent after every…
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Taxonomy
TopicsOptimization and Search Problems · Mobile Ad Hoc Networks · Mobile Agent-Based Network Management
