--- _id: '22510' abstract: - lang: eng text: '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.' author: - first_name: Shouwei full_name: Li, Shouwei last_name: Li - first_name: Christine full_name: Markarian, Christine last_name: Markarian - first_name: Friedhelm full_name: Meyer auf der Heide, Friedhelm id: '15523' last_name: Meyer auf der Heide - first_name: Pavel full_name: Podlipyan, Pavel last_name: Podlipyan citation: ama: Li S, Markarian C, Meyer auf der Heide F, Podlipyan P. A continuous strategy for collisionless gathering. Theoretical Computer Science. 2021;852:41-60. doi:10.1016/j.tcs.2020.10.037 apa: Li, S., Markarian, C., Meyer auf der Heide, F., & Podlipyan, P. (2021). A continuous strategy for collisionless gathering. Theoretical Computer Science, 852, 41–60. https://doi.org/10.1016/j.tcs.2020.10.037 bibtex: '@article{Li_Markarian_Meyer auf der Heide_Podlipyan_2021, title={A continuous strategy for collisionless gathering}, volume={852}, DOI={10.1016/j.tcs.2020.10.037}, journal={Theoretical Computer Science}, author={Li, Shouwei and Markarian, Christine and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}, year={2021}, pages={41–60} }' chicago: 'Li, Shouwei, Christine Markarian, Friedhelm Meyer auf der Heide, and Pavel Podlipyan. “A Continuous Strategy for Collisionless Gathering.” Theoretical Computer Science 852 (2021): 41–60. https://doi.org/10.1016/j.tcs.2020.10.037.' ieee: S. Li, C. Markarian, F. Meyer auf der Heide, and P. Podlipyan, “A continuous strategy for collisionless gathering,” Theoretical Computer Science, vol. 852, pp. 41–60, 2021. mla: Li, Shouwei, et al. “A Continuous Strategy for Collisionless Gathering.” Theoretical Computer Science, vol. 852, 2021, pp. 41–60, doi:10.1016/j.tcs.2020.10.037. short: S. Li, C. Markarian, F. Meyer auf der Heide, P. Podlipyan, Theoretical Computer Science 852 (2021) 41–60. date_created: 2021-06-28T09:24:15Z date_updated: 2022-01-06T06:55:35Z department: - _id: '63' doi: 10.1016/j.tcs.2020.10.037 intvolume: ' 852' keyword: - Local algorithms - Distributed algorithms - Collisionless gathering - Mobile robots - Multiagent system language: - iso: eng page: 41-60 publication: Theoretical Computer Science publication_identifier: issn: - 0304-3975 publication_status: published status: public title: A continuous strategy for collisionless gathering type: journal_article user_id: '15415' volume: 852 year: '2021' ... --- _id: '22511' abstract: - lang: eng text: "In this paper, we reconsider the well-known discrete, round-based Go-To-The-Center algorithm due to Ando, Suzuki, and Yamashita [2] for gathering n autonomous mobile robots with limited viewing range in the plane. Remarquably, this algorithm exploits the fact that during its execution, many collisions of robots occur. Such collisions are interpreted as a success because it is assumed that such collided robots behave the same from now on. This is acceptable under the assumption that each robot is represented by a single point. Otherwise, collisions should be avoided. In this paper, we consider a continuous Go-To-The-Center algorithm in which the robots continuously observe the positions of their neighbors and adapt their speed (assuming a speed limit) and direction. Our first results are time bounds of O(n2) for gathering in two dimensions Euclidean space, and Θ(n) for the one dimension. Our main contribution is the introduction and evaluation of a continuous algorithm which performs Go-To-The-Center considering only the neighbors of a robot with respect to the Gabriel subgraph of the visibility graph, i.e. Go-To-The-Gabriel-Center algorithm. We show that this modification still correctly executes gathering in one and two dimensions, with the same time bounds as above. Simulations exhibit a severe difference of the behavior of the Go-To-The-Center and the Go-To-The-Gabriel-Center algorithms: Whereas lots of collisions occur during a run of the Go-To-The-Center algorithm, typically only one, namely the final collision occurs during a run of the Go-To-The-Gabriel-Center algorithm. We can prove this “collisionless property” of the Go-To-The-Gabriel-Center algorithm for one dimension. In two-dimensional Euclidean space, we conjecture that the “collisionless property” holds for almost every initial configuration. We support our conjecture with measurements obtained from the simulation where robots execute both continuous Go-To-The-Center and Go-To-The-Gabriel-Center algorithms.\r\n" author: - first_name: Shouwei full_name: Li, Shouwei last_name: Li - first_name: Friedhelm full_name: Meyer auf der Heide, Friedhelm id: '15523' last_name: Meyer auf der Heide - first_name: Pavel full_name: Podlipyan, Pavel last_name: Podlipyan citation: ama: Li S, Meyer auf der Heide F, Podlipyan P. The impact of the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots. Theoretical Computer Science. 2021;852:29-40. doi:10.1016/j.tcs.2020.11.009 apa: Li, S., Meyer auf der Heide, F., & Podlipyan, P. (2021). The impact of the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots. Theoretical Computer Science, 852, 29–40. https://doi.org/10.1016/j.tcs.2020.11.009 bibtex: '@article{Li_Meyer auf der Heide_Podlipyan_2021, title={The impact of the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots}, volume={852}, DOI={10.1016/j.tcs.2020.11.009}, journal={Theoretical Computer Science}, author={Li, Shouwei and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}, year={2021}, pages={29–40} }' chicago: 'Li, Shouwei, Friedhelm Meyer auf der Heide, and Pavel Podlipyan. “The Impact of the Gabriel Subgraph of the Visibility Graph on the Gathering of Mobile Autonomous Robots.” Theoretical Computer Science 852 (2021): 29–40. https://doi.org/10.1016/j.tcs.2020.11.009.' ieee: S. Li, F. Meyer auf der Heide, and P. Podlipyan, “The impact of the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots,” Theoretical Computer Science, vol. 852, pp. 29–40, 2021. mla: Li, Shouwei, et al. “The Impact of the Gabriel Subgraph of the Visibility Graph on the Gathering of Mobile Autonomous Robots.” Theoretical Computer Science, vol. 852, 2021, pp. 29–40, doi:10.1016/j.tcs.2020.11.009. short: S. Li, F. Meyer auf der Heide, P. Podlipyan, Theoretical Computer Science 852 (2021) 29–40. date_created: 2021-06-28T09:34:45Z date_updated: 2022-01-06T06:55:35Z department: - _id: '63' doi: 10.1016/j.tcs.2020.11.009 intvolume: ' 852' keyword: - Local algorithms - Distributed algorithms - Collisionless gathering - Mobile robots - Multiagent system language: - iso: eng page: 29-40 publication: Theoretical Computer Science publication_identifier: issn: - 0304-3975 publication_status: published status: public title: The impact of the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots type: journal_article user_id: '15415' volume: 852 year: '2021' ...