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

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Algorithms — ESA '96 (ESA 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1136))

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Abstract

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(n 6) 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(n 4) algorithm for the GMP1R on a tree. Moreover, we give an O(n 3) 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.

Partially supported by Progetto MURST 40%, Algoritmi, Modelli di Calcolo e Strutture Informative.

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References

  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 http://www.unisa.it/papers/robot.ps.gz).

    Google Scholar 

  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.

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  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. 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. J.T. Schwartz, M. Sharir, and J. Hopcroft, Planning, Geometry, and Complexity of Robot Motion, Ablex, Norwood NJ, 1987.

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081, Baronissi, Italy

    Vincenzo Auletta, Domenico Parente & Pino Persiano

Authors
  1. Vincenzo Auletta
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  2. Domenico Parente
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  3. Pino Persiano
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Editor information

Josep Diaz Maria Serna

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© 1996 Springer-Verlag Berlin Heidelberg

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Auletta, V., Parente, D., Persiano, P. (1996). A new approach to optimal planning of robot motion on a tree with obstacles. In: Diaz, J., Serna, M. (eds) Algorithms — ESA '96. ESA 1996. Lecture Notes in Computer Science, vol 1136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61680-2_80

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  • DOI: https://doi.org/10.1007/3-540-61680-2_80

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61680-1

  • Online ISBN: 978-3-540-70667-0

  • eBook Packages: Springer Book Archive

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