arXiv:2509.10711v2 Announce Type: replace Abstract: We consider the benchmarking problem of gathering in an $(N,f)$-fault system consisting of $N$ robots, of which at most $f$ may fail at any execution. The {\em traditional} version asks $N-f$ non-faulty robots to gather at a point not known a priori. The recently studied {\em indulgent} version asks $N-f$ non-faulty robots to gather at the location of a faulty one. Indulgent gathering is impossible in a $(2,1)$-crash system in the $LUMI$ model under semi-synchrony, even when infinitely many colors and coordinate axis agreement are available. In this paper, we establish four results for indulgent gathering under asynchrony in $LUMI$, considering a {\em mobility fault} model in which a robot crash only impacts its mobility but not the operation of the light. We first show that indulgent gathering is impossible in a $(2,1)$-mobility system using 2-colored lights, and then give an optimal solution w.r.t. the number of colors using 3-colored lights. We then give two deterministic algorithms for an $(N,f)$-mobility system, $fSource：https://arxiv.org/abs/2509.10711
My favorites