A new approach to optimal planning of robot motion on a tree with obstacles
In this paper we study the Graph Motion Planning of 1 Robot problem (GMP1R) on a tree. This problem consists in computing a minimum cost plan for moving a robot from one vertex to another in a tree whose vertices can have movable obstacles.
Papadimitriou et alt. [FOCS 94] introduced the problem and gave an algorithm for the GMP1R on a tree. Their approach is based on flow arguments and yields an algorithm that solves O(n6) mincost flow problems on graphs with O(n) vertices. They also give a 7 approximation algorithm that solves O(n) mincost flow problems on graphs with O(n) vertices.
We propose a new dynamic programming approach to GMP1R on a tree. Based on this approach we give a O(n4) algorithm for the GMP1R on a tree. Moreover, we give an O(n3) approximation algorithm that obtains a solution that is within a 7 factor from the optimum.
We also discuss extensions of our work and pose a new open problem.
KeywordsLeft Part Critical Path Short Path Problem Dynamic Programming Approach Outward Move
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