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arXiv · 2304.05722

Stand-Up Indulgent Gathering on Lines

Quentin Bramas·Sayaka Kamei·Anissa Lamani·Sébastien Tixeuil
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Abstract

We consider a variant of the crash-fault gathering problem called stand-up indulgent gathering (SUIG). In this problem, a group of mobile robots must eventually gather at a single location, which is not known in advance. If no robots crash, they must all meet at the same location. However, if one or more robots crash at a single location, all non-crashed robots must eventually gather at that location. The SUIG problem was first introduced for robots operating in a two-dimensional continuous Euclidean space, with most solutions relying on the ability of robots to move a prescribed (real) distance at each time instant. In this paper, we investigate the SUIG problem for robots operating in a discrete universe (i.e., a graph) where they can only move one unit of distance (i.e., to an adjacent node) at each time instant. Specifically, we focus on line-shaped networks and characterize the solvability of the SUIG problem for oblivious robots without multiplicity detection.

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Quentin Bramas, Sayaka Kamei, Anissa Lamani, Sébastien Tixeuil. 2023-04-12. Stand-Up Indulgent Gathering on Lines. https://arxiv.org/abs/2304.05722

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