TY - GEN
T1 - The parameterized complexity of motion planning for snake-like robots
AU - Gupta, Siddharth
AU - Sa'ar, Guy
AU - Zehavi, Meirav
N1 - Funding Information:
∗Supported in part by the Zuckerman STEM Leadership Program †Supported in part by the Frankel Foundation ‡Supported by Israel Science Foundation (ISF) grant no. 1176/18
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85074906483&partnerID=8YFLogxK
U2 - 10.24963/ijcai.2019/786
DO - 10.24963/ijcai.2019/786
M3 - Conference contribution
AN - SCOPUS:85074906483
T3 - IJCAI International Joint Conference on Artificial Intelligence
SP - 5670
EP - 5676
BT - Proceedings of the 28th International Joint Conference on Artificial Intelligence, IJCAI 2019
A2 - Kraus, Sarit
PB - International Joint Conferences on Artificial Intelligence
T2 - 28th International Joint Conference on Artificial Intelligence, IJCAI 2019
Y2 - 10 August 2019 through 16 August 2019
ER -