Gathering in 1-Interval Connected Graphs

Michail, Othon ORCID: 0000-0002-6234-3960, Spirakis, Paul G and Theofilatos, Michail ORCID: 0000-0002-3699-0179 Gathering in 1-Interval Connected Graphs.

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Abstract

We examine the problem of gathering $k \geq 2$ agents (or multi-agent rendezvous) in dynamic graphs which may change in every synchronous round but remain always connected ($1$-interval connectivity) [KLO10]. The agents are identical and without explicit communication capabilities, and are initially positioned at different nodes of the graph. The problem is for the agents to gather at the same node, not fixed in advance. We first show that the problem becomes impossible to solve if the graph has a cycle. In light of this, we study a relaxed version of this problem, called weak gathering. We show that only in unicyclic graphs weak gathering is solvable, and we provide a deterministic algorithm for this problem that runs in polynomial number of rounds.

Item Type:	Article
Uncontrolled Keywords:	cs.DC, cs.DC, cs.MA
Depositing User:	Symplectic Admin
Date Deposited:	26 Aug 2020 10:11
Last Modified:	18 Jan 2023 23:36
Related URLs:	Author
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3098917