{"title":"Gathering Anonymous, Oblivious Robots on a Grid","citation":{"apa":"Fischer, M., Jung, D., &#38; Meyer auf der Heide, F. (2017). Gathering Anonymous, Oblivious Robots on a Grid. <i>ArXiv:1702.03400</i>.","mla":"Fischer, Matthias, et al. “Gathering Anonymous, Oblivious Robots on a Grid.” <i>ArXiv:1702.03400</i>, 2017.","chicago":"Fischer, Matthias, Daniel Jung, and Friedhelm Meyer auf der Heide. “Gathering Anonymous, Oblivious Robots on a Grid.” <i>ArXiv:1702.03400</i>, 2017.","bibtex":"@article{Fischer_Jung_Meyer auf der Heide_2017, title={Gathering Anonymous, Oblivious Robots on a Grid}, journal={arXiv:1702.03400}, author={Fischer, Matthias and Jung, Daniel and Meyer auf der Heide, Friedhelm}, year={2017} }","ama":"Fischer M, Jung D, Meyer auf der Heide F. Gathering Anonymous, Oblivious Robots on a Grid. <i>arXiv:170203400</i>. 2017.","ieee":"M. Fischer, D. Jung, and F. Meyer auf der Heide, “Gathering Anonymous, Oblivious Robots on a Grid,” <i>arXiv:1702.03400</i>. 2017.","short":"M. Fischer, D. Jung, F. Meyer auf der Heide, ArXiv:1702.03400 (2017)."},"publication":"arXiv:1702.03400","abstract":[{"lang":"eng","text":"We consider a swarm of $n$ autonomous mobile robots, distributed on a\r\n2-dimensional grid. A basic task for such a swarm is the gathering process: All\r\nrobots have to gather at one (not predefined) place. A common local model for\r\nextremely simple robots is the following: The robots do not have a common\r\ncompass, only have a constant viewing radius, are autonomous and\r\nindistinguishable, can move at most a constant distance in each step, cannot\r\ncommunicate, are oblivious and do not have flags or states. The only gathering\r\nalgorithm under this robot model, with known runtime bounds, needs\r\n$\\mathcal{O}(n^2)$ rounds and works in the Euclidean plane. The underlying time\r\nmodel for the algorithm is the fully synchronous $\\mathcal{FSYNC}$ model. On\r\nthe other side, in the case of the 2-dimensional grid, the only known gathering\r\nalgorithms for the same time and a similar local model additionally require a\r\nconstant memory, states and \"flags\" to communicate these states to neighbors in\r\nviewing range. They gather in time $\\mathcal{O}(n)$.\r\n  In this paper we contribute the (to the best of our knowledge) first\r\ngathering algorithm on the grid that works under the same simple local model as\r\nthe above mentioned Euclidean plane strategy, i.e., without memory (oblivious),\r\n\"flags\" and states. We prove its correctness and an $\\mathcal{O}(n^2)$ time\r\nbound in the fully synchronous $\\mathcal{FSYNC}$ time model. This time bound\r\nmatches the time bound of the best known algorithm for the Euclidean plane\r\nmentioned above. We say gathering is done if all robots are located within a\r\n$2\\times 2$ square, because in $\\mathcal{FSYNC}$ such configurations cannot be\r\nsolved."}],"_id":"17811","date_updated":"2022-01-06T06:53:20Z","date_created":"2020-08-11T13:48:38Z","language":[{"iso":"eng"}],"type":"preprint","user_id":"15415","author":[{"full_name":"Fischer, Matthias","last_name":"Fischer","first_name":"Matthias","id":"146"},{"first_name":"Daniel","full_name":"Jung, Daniel","last_name":"Jung","id":"37827"},{"id":"15523","first_name":"Friedhelm","full_name":"Meyer auf der Heide, Friedhelm","last_name":"Meyer auf der Heide"}],"department":[{"_id":"63"}],"status":"public","year":"2017"}