Proceedings 35th Annual Symposium on Foundations of Computer Science (1994)
Santa Fe, NM, USA
Nov. 20, 1994 to Nov. 22, 1994
C.H. Papadimitriou , Dept. of Comput. Sci.&Eng., California Univ., San Diego, La Jolla, CA, USA
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.
complexity, motion planning, undirected graph, vertices, mobile robot, single movable obstacle, vertex, simple abstraction, adjacencies
C. Papadimitriou, H. Tamaki, M. Sudan and P. Raghavan, "Motion planning on a graph," Proceedings 35th Annual Symposium on Foundations of Computer Science(FOCS), Santa Fe, NM, USA, 1994, pp. 511-520.