{"type":"preprint","user_id":"15415","external_id":{"arxiv":["1510.05454"]},"status":"public","abstract":[{"lang":"eng","text":"We consider the following variant of the two dimensional gathering problem\r\nfor swarms of robots: Given a swarm of $n$ indistinguishable, point shaped\r\nrobots on a two dimensional grid. Initially, the robots form a closed chain on\r\nthe grid and must keep this connectivity during the whole process of their\r\ngathering. Connectivity means, that neighboring robots of the chain need to be\r\npositioned at the same or neighboring points of the grid. In our model,\r\ngathering means to keep shortening the chain until the robots are located\r\ninside a $2\\times 2$ subgrid. Our model is completely local (no global control,\r\nno global coordinates, no compass, no global communication or vision, \\ldots).\r\nEach robot can only see its next constant number of left and right neighbors on\r\nthe chain. This fixed constant is called the \\emph{viewing path length}. All\r\nits operations and detections are restricted to this constant number of robots.\r\nOther robots, even if located at neighboring or the same grid point cannot be\r\ndetected. Only based on the relative positions of its detectable chain\r\nneighbors, a robot can decide to obtain a certain state. Based on this state\r\nand their local knowledge, the robots do local modifications to the chain by\r\nmoving to neighboring grid points without breaking the chain. These\r\nmodifications are performed without the knowledge whether they lead to a global\r\nprogress or not. We assume the fully synchronous $\\mathcal{FSYNC}$ model. For\r\nthis problem, we present a gathering algorithm which needs linear time. This\r\nresult generalizes the result from \\cite{hopper}, where an open chain with\r\nspecified distinguishable (and fixed) endpoints is considered."}],"date_created":"2020-04-07T07:20:46Z","date_updated":"2022-01-06T06:52:50Z","publication":"arXiv:1510.05454","title":"Gathering a Closed Chain of Robots on a Grid","department":[{"_id":"63"}],"year":"2015","author":[{"first_name":"Sebastian","full_name":"Abshoff, Sebastian","last_name":"Abshoff"},{"last_name":"Cord-Landwehr","full_name":"Cord-Landwehr, Andreas ","first_name":"Andreas "},{"id":"146","full_name":"Fischer, Matthias","last_name":"Fischer","first_name":"Matthias"},{"id":"37827","first_name":"Daniel","full_name":"Jung, Daniel","last_name":"Jung"},{"id":"15523","first_name":"Friedhelm","full_name":"Meyer auf der Heide, Friedhelm","last_name":"Meyer auf der Heide"}],"citation":{"ama":"Abshoff S, Cord-Landwehr A, Fischer M, Jung D, Meyer auf der Heide F. Gathering a Closed Chain of Robots on a Grid. <i>arXiv:151005454</i>. 2015.","chicago":"Abshoff, Sebastian, Andreas  Cord-Landwehr, Matthias Fischer, Daniel Jung, and Friedhelm Meyer auf der Heide. “Gathering a Closed Chain of Robots on a Grid.” <i>ArXiv:1510.05454</i>, 2015.","short":"S. Abshoff, A. Cord-Landwehr, M. Fischer, D. Jung, F. Meyer auf der Heide, ArXiv:1510.05454 (2015).","ieee":"S. Abshoff, A. Cord-Landwehr, M. Fischer, D. Jung, and F. Meyer auf der Heide, “Gathering a Closed Chain of Robots on a Grid,” <i>arXiv:1510.05454</i>. 2015.","apa":"Abshoff, S., Cord-Landwehr, A., Fischer, M., Jung, D., &#38; Meyer auf der Heide, F. (2015). Gathering a Closed Chain of Robots on a Grid. <i>ArXiv:1510.05454</i>.","bibtex":"@article{Abshoff_Cord-Landwehr_Fischer_Jung_Meyer auf der Heide_2015, title={Gathering a Closed Chain of Robots on a Grid}, journal={arXiv:1510.05454}, author={Abshoff, Sebastian and Cord-Landwehr, Andreas  and Fischer, Matthias and Jung, Daniel and Meyer auf der Heide, Friedhelm}, year={2015} }","mla":"Abshoff, Sebastian, et al. “Gathering a Closed Chain of Robots on a Grid.” <i>ArXiv:1510.05454</i>, 2015."},"_id":"16449","language":[{"iso":"eng"}]}