The parameterized complexity of motion planning for snake-like robots

Siddharth Gupta, Guy Sa'ar, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 “snakelike” 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 kO(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.

Original languageEnglish
Title of host publicationProceedings of the 28th International Joint Conference on Artificial Intelligence, IJCAI 2019
EditorsSarit Kraus
PublisherInternational Joint Conferences on Artificial Intelligence
Pages5670-5676
Number of pages7
ISBN (Electronic)9780999241141
DOIs
StatePublished - 1 Jan 2019
Event28th International Joint Conference on Artificial Intelligence, IJCAI 2019 - Macao, China
Duration: 10 Aug 201916 Aug 2019

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
Volume2019-August
ISSN (Print)1045-0823

Conference

Conference28th International Joint Conference on Artificial Intelligence, IJCAI 2019
Country/TerritoryChina
CityMacao
Period10/08/1916/08/19

ASJC Scopus subject areas

  • Artificial Intelligence

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