10.1016/j.tcs.2020.10.037
Li, Shouwei
Shouwei
Li
Markarian, Christine
Christine
Markarian
Meyer auf der Heide, Friedhelm
Friedhelm
Meyer auf der Heide
Podlipyan, Pavel
Pavel
Podlipyan
A continuous strategy for collisionless gathering
2021
2021-06-28T09:24:15Z
2021-06-28T09:47:26Z
journal_article
https://ris.uni-paderborn.de/record/22510
https://ris.uni-paderborn.de/record/22510.json
0304-3975
Over the past decades, the Gathering problem, which asks to gather a group of robots in finite time given some restrictions, has been intensively studied. In this paper, we are given a group of n autonomous, dimensionless, deterministic, and anonymous robots, with bounded viewing range. Assuming a continuous time model, the goal is to gather these robots into one point in finite time. We introduce a simple convergence criterion that defines a new class of algorithms which perform gathering in O(nd) time, where d is the diameter of the initial robot configuration. We show that some gathering algorithms in the literature belong to this class and propose two new algorithms that belong to this class and have quadratic running time, namely, Go-To-The-Relative-Center algorithm (GTRC) and Safe-Go-To-The-Relative-Center algorithm (S-GTRC). We prove that the latter can perform gathering without collision by using a slightly more complex robot model: non oblivious, chiral, and luminous (i.e. robots have observable external memory, as in [8]). We also consider a variant of the Gathering problem, the Near-Gathering problem, in which robots must get close to each other without colliding. We show that S-GTRC solves the Near-Gathering problem in quadratic time and assumes a weaker robot model than the one assumed in the current state-of-the-art.