A new approach to optimal planning of robot motion on a tree with obstacles

  • Vincenzo Auletta
  • Domenico Parente
  • Pino Persiano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1136)


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.


Left Part Critical Path Short Path Problem Dynamic Programming Approach Outward Move 
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  1. 1.
    V. Auletta, D. Parente, G. Persiano Optimal Planning of Robot Motion on a Tree with Obstacles, Technical Report Università di Salerno, 1995 (a postscript file of this report can be downloaded at the URL Scholar
  2. 2.
    D. Kornhauser, G. Miller, and P. Spirakis, Coordinating Pebble Motion on Graphs, the Diameter of Permutations Groups, and Applications, in Proc. of 25-th IEEE Symp. on Found. of Comp. Sc., (FOCS), 241–250, 1984.Google Scholar
  3. 3.
    C. Papadimitriou, P. Raghavan, M. Sudan and H. Tamaki, Motion Planning on a Graph, in Proc. of 35-th IEEE Symp. on Found. of Comp. Sc., (FOCS), 511–520 1994.Google Scholar
  4. 4.
    D. Ratner and M. Warmuth, Finding a Shortest Solution for the (N×N)-Extension of the 15 Puzzle is NP-hard, Journal of Symbolic Computation 10:111–137, 1990.Google Scholar
  5. 5.
    J.T. Schwartz, M. Sharir, and J. Hopcroft, Planning, Geometry, and Complexity of Robot Motion, Ablex, Norwood NJ, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Vincenzo Auletta
    • 1
  • Domenico Parente
    • 1
  • Pino Persiano
    • 1
  1. 1.Dipartimento di Informatica ed ApplicazioniUniversità di SalernoBaronissiItaly

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