{"doi":"10.1007/978-3-030-54921-3_4","file":[{"relation":"main_file","date_updated":"2020-07-31T08:22:16Z","file_size":505712,"content_type":"application/pdf","file_id":"17504","file_name":"localGathering.pdf","creator":"janniksu","date_created":"2020-07-31T08:22:16Z","access_level":"closed","success":1}],"department":[{"_id":"63"}],"language":[{"iso":"eng"}],"_id":"16968","conference":{"start_date":"2020-06-29","name":"SIROCCO 2020","location":"Paderborn","end_date":"2020-07-01"},"has_accepted_license":"1","user_id":"38705","title":"Local Gathering of Mobile Robots in Three Dimensions","external_id":{"arxiv":["arXiv:2005.07495"]},"citation":{"ieee":"M. Braun, J. Castenow, and F. Meyer auf der Heide, “Local Gathering of Mobile Robots in Three Dimensions,” in <i>Proceedings of the 27th Conference on Structural Information and Communication Complexity (SIROCCO)</i>, Paderborn, 2020.","mla":"Braun, Michael, et al. “Local Gathering of Mobile Robots in Three Dimensions.” <i>Proceedings of the 27th Conference on Structural Information and Communication Complexity (SIROCCO)</i>, Springer, 2020, doi:<a href=\"https://doi.org/10.1007/978-3-030-54921-3_4\">10.1007/978-3-030-54921-3_4</a>.","chicago":"Braun, Michael, Jannik Castenow, and Friedhelm Meyer auf der Heide. “Local Gathering of Mobile Robots in Three Dimensions.” In <i>Proceedings of the 27th Conference on Structural Information and Communication Complexity (SIROCCO)</i>. Springer, 2020. <a href=\"https://doi.org/10.1007/978-3-030-54921-3_4\">https://doi.org/10.1007/978-3-030-54921-3_4</a>.","ama":"Braun M, Castenow J, Meyer auf der Heide F. Local Gathering of Mobile Robots in Three Dimensions. In: <i>Proceedings of the 27th Conference on Structural Information and Communication Complexity (SIROCCO)</i>. Springer; 2020. doi:<a href=\"https://doi.org/10.1007/978-3-030-54921-3_4\">10.1007/978-3-030-54921-3_4</a>","apa":"Braun, M., Castenow, J., &#38; Meyer auf der Heide, F. (2020). Local Gathering of Mobile Robots in Three Dimensions. In <i>Proceedings of the 27th Conference on Structural Information and Communication Complexity (SIROCCO)</i>. Paderborn: Springer. <a href=\"https://doi.org/10.1007/978-3-030-54921-3_4\">https://doi.org/10.1007/978-3-030-54921-3_4</a>","short":"M. Braun, J. Castenow, F. Meyer auf der Heide, in: Proceedings of the 27th Conference on Structural Information and Communication Complexity (SIROCCO), Springer, 2020.","bibtex":"@inproceedings{Braun_Castenow_Meyer auf der Heide_2020, title={Local Gathering of Mobile Robots in Three Dimensions}, DOI={<a href=\"https://doi.org/10.1007/978-3-030-54921-3_4\">10.1007/978-3-030-54921-3_4</a>}, booktitle={Proceedings of the 27th Conference on Structural Information and Communication Complexity (SIROCCO)}, publisher={Springer}, author={Braun, Michael and Castenow, Jannik and Meyer auf der Heide, Friedhelm}, year={2020} }"},"author":[{"last_name":"Braun","full_name":"Braun, Michael","first_name":"Michael"},{"id":"38705","last_name":"Castenow","full_name":"Castenow, Jannik","first_name":"Jannik"},{"last_name":"Meyer auf der Heide","id":"15523","first_name":"Friedhelm","full_name":"Meyer auf der Heide, Friedhelm"}],"abstract":[{"lang":"eng","text":"In this work, we initiate the research about the Gathering problem for robots\r\nwith limited viewing range in the three-dimensional Euclidean space. In the\r\nGathering problem, a set of initially scattered robots is required to gather at\r\nthe same position. The robots' capabilities are very restricted -- they do not\r\nagree on any coordinate system or compass, have a limited viewing range, have\r\nno memory of the past and cannot communicate. We study the problem in two\r\ndifferent time models, in FSYNC (fully synchronized discrete rounds) and the\r\ncontinuous time model. For FSYNC, we introduce the 3D-Go-To-The-Center-strategy\r\nand prove a runtime of $\\Theta(n^2)$ that matches the currently best runtime\r\nbound for the same model in the Euclidean plane [SPAA'11]. Our main result is\r\nthe generalization of contracting strategies (continuous time) from\r\n[Algosensors'17] to three dimensions. In contracting strategies, every robot\r\nthat is located on the global convex hull of all robots' positions moves with\r\nfull speed towards the inside of the convex hull. We prove a runtime bound of\r\n$O(\\Delta \\cdot n^{3/2})$ for any three-dimensional contracting strategy, where\r\n$\\Delta$ denotes the diameter of the initial configuration. This comes up to a\r\nfactor of $\\sqrt{n}$ close to the lower bound of $\\Omega (\\Delta \\cdot n)$\r\nwhich is already true in two dimensions. In general, it might be hard for\r\nrobots with limited viewing range to decide whether they are located on the\r\nglobal convex hull and which movement maintains the connectivity of the swarm,\r\nrendering the design of concrete contracting strategies a challenging task. We\r\nprove that the continuous variant of 3D-Go-To-The-Center is contracting and\r\nkeeps the swarm connected. Moreover, we give a simple design criterion for\r\nthree-dimensional contracting strategies that maintains the connectivity of the\r\nswarm and introduce an exemplary strategy based on this criterion."},{"text":"Best Student Paper Award","lang":"eng"}],"date_created":"2020-05-18T06:48:35Z","file_date_updated":"2020-07-31T08:22:16Z","type":"conference","publication":"Proceedings of the 27th Conference on Structural Information and Communication Complexity (SIROCCO)","ddc":["000"],"year":"2020","status":"public","date_updated":"2022-01-06T06:53:00Z","publisher":"Springer"}