2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1994)

Santa Fe, NM, USA

Nov. 20, 1994 to Nov. 22, 1994

ISBN: 0-8186-6580-7

pp: 511-520

C.H. Papadimitriou , Dept. of Comput. Sci.&Eng., California Univ., San Diego, La Jolla, CA, USA

ABSTRACT

We are given a connected, undirected graph G on n vertices. There is a mobile robot on one of the vertices; this vertex is labeled s. Each of several other vertices contains a single movable obstacle. The robot and the obstacles may only reside at vertices, although they may be moved across edges. A vertex may never contain more than one object (robot/obstacle). In one step, we may move either the robot or one of the obstacles from its current position /spl upsi/ to a vacant vertex adjacent to v. Our goal is to move the robot to a designated vertex t using the smallest number of steps possible. The problem is a simple abstraction of a robot motion planning problem, with the geometry replaced by the adjacencies in the graph. We point out its connections to robot motion planning. We study its complexity, giving exact and approximate algorithms for several cases.

INDEX TERMS

complexity, motion planning, undirected graph, vertices, mobile robot, single movable obstacle, vertex, simple abstraction, adjacencies

CITATION

C.H. Papadimitriou,
H. Tamaki,
M. Sudan,
P. Raghavan,
"Motion planning on a graph",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 511-520, 1994, doi:10.1109/SFCS.1994.365740SEARCH