{"type":"ScholarlyArticle","title":"The Parameterized Complexity of Motion Planning for Snake-Like Robots","authors":[{"name":"Siddharth Gupta","slug":"siddharth-gupta","given":"Siddharth","family":"Gupta","affiliation":"Ben-Gurion University of the Negev , Israel"},{"name":"Guy Sa'ar","slug":"guy-sa-ar","given":"Guy","family":"Sa'ar","affiliation":"Ben-Gurion University of the Negev , Israel"},{"name":"Meirav Zehavi","slug":"meirav-zehavi","given":"Meirav","family":"Zehavi","affiliation":"Ben-Gurion University of the Negev , Israel"}],"abstract":"We study a motion-planning problem inspired by the game Snake that models scenarios like the transportation of linked wagons towed by a locomotor to the movement of a group of agents that travel in an ``ant-like'' fashion. Given a ``snake-like'' robot with initial and final positions in an environment modeled by a graph, our goal is to decide whether the robot can reach the final position from the initial position without intersecting itself. Already on grid graphs, this problem is PSPACE-complete [Biasi and Ophelders, 2018]. Nevertheless, we prove that even on general graphs, it is solvable in time k^{O(k)}|I|^{O(1)} where k is the size of the robot, and |I| is the input size. Towards this, we give a novel application of color-coding to sparsify the configuration graph of the problem. We also show that the problem is unlikely to have a polynomial kernel even on grid graphs, but it admits a treewidth-reduction procedure. To the best of our knowledge, the study of the parameterized complexity of motion problems has been~largely~neglected, thus our work is pioneering in this regard.","doi":"10.24963/ijcai.2019/786","url":"https://ijcai.org/proceedings/2019/786","pdf":"https://ijcai.org/proceedings/2019/0786.pdf","markdown":"https://ijcai.org/proceedings/2019/786.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/786","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Robotics","track":"Main track","number":786,"pages":{"first":5670,"last":5676},"keywords":["Multidisciplinary Topics and Applications: Computer Games","Robotics: Motion and Path Planning","Planning and Scheduling: Planning Algorithms"],"videos":[],"references":[{"position":1,"raw":"[Alon et al., 1995] Noga Alon, Raphael Yuster, and Uri Zwick. 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