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arXiv · 2509.06064

Gathering in Non-Vertex-Transitive Graphs Under Round Robin

Serafino Cicerone·Alessia Di Fonso·Gabriele Di Stefano·Alfredo Navarra
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Abstract

The Gathering problem for a swarm of robots asks for a distributed algorithm that brings such entities to a common place, not known in advance. We consider the well-known OBLOT model with robots constrained to move along the edges of a graph, hence gathering in one vertex, eventually. Despite the classical setting under which the problem has been usually approached, we consider the `hostile' case where: i) the initial configuration may contain multiplicities, i.e. more than one robot may occupy the same vertex; ii) robots cannot detect multiplicities. As a scheduler for robot activation, we consider the "favorable" round-robin case, where robots are activated one at a time. Our objective is to achieve a complete characterization of the problem in the broad context of non-vertex-transitive graphs, i.e., graphs where the vertices are partitioned into at least two different classes of equivalence. We provide a resolution algorithm for any configuration of robots moving on such graphs, along with its correctness. Furthermore, we analyze its time complexity.

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Serafino Cicerone, Alessia Di Fonso, Gabriele Di Stefano, Alfredo Navarra. 2025-09-07. Gathering in Non-Vertex-Transitive Graphs Under Round Robin. https://arxiv.org/abs/2509.06064

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