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Competitive Exploration of Rectilinear Polygons

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Fundamentals of Computation Theory (FCT 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2751))

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Abstract

Exploring a polygon with a robot, when the robot does not have a map of its surroundings can be viewed as an online problem. Typical for online problems is that you must make decisions based on past events without complete information about the future. In our case the robot does not have complete information about the environment. Competitive analysis can be used to measure the performance of methods solving online problems. The competitive ratio of such a method is the ratio between the method’s performance and the performance of the best method having full knowledge of the future. We are interested in obtaining good upper bounds on the competitive ratio of exploring polygons and prove a 3/2-competitive strategy for exploring a simple rectilinear polygon in the L 1 metric.

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References

  1. Betke, M., Rivest, R.L., Singh, M.: Piecemeal Learning of an Unknown Environment. Machine Learning 18(2-3), 231–254 (1995)

    Article  Google Scholar 

  2. Chan, K.-F., Lam, T.W.: An on-line algorithm for navigating in an unknown environment. International Journal of Computational Geometry & Applications 3, 227–244 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chin, W., Ntafos, S.: OptimumWatchman Routes. Information Processing Letters 28, 39–44 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  4. Deng, X., Kameda, T., Papadimitriou, C.H.: How to Learn an Unknown Environment I: The Rectilinear Case. Journal of the ACM 45(2), 215–245 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hammar, M., Nilsson, B.J., Schuierer, S.: Improved Exploration of Rectilinear Polygons. Nordic Journal of Computing 9(1), 32–53 (2002)

    MATH  MathSciNet  Google Scholar 

  6. Hoffmann, F., Icking, C., Klein, R., Kriegel, K.: The Polygon Exploration Problem. SIAM Journal on Computing 31(2), 577–600 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kleinberg, J.M.: On-line search in a simple polygon. In: Proc. of 5th ACM-SIAM Symp. on Discrete Algorithms, pp. 8–15 (1994)

    Google Scholar 

  8. Mei, A., Igarashi, Y.: An Efficient Strategy for Robot Navigation in Unknown Environment. Inform. Process. Lett. 52, 51–56 (1994)

    Article  Google Scholar 

  9. Papadimitriou, C.H., Yannakakis, M.: Shortest Paths Without a Map. Theoret. Comput. Sci. 84(1), 127–150 (1991)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Salerno University, Baronissi (SA), 84081, Italy

    Mikael Hammar

  2. Technology and Society, Malmö University College, S-205 06, Malmö, Sweden

    Bengt J. Nilsson & Mia Persson

Authors
  1. Mikael Hammar
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  2. Bengt J. Nilsson
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  3. Mia Persson
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Lund University, 22100, Lund, Sweden

    Andrzej Lingas

  2. School of Technology and Society, Malmö University, SE-205 06, Malmö, Sweden

    Bengt J. Nilsson

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© 2003 Springer-Verlag Berlin Heidelberg

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Hammar, M., Nilsson, B.J., Persson, M. (2003). Competitive Exploration of Rectilinear Polygons. In: Lingas, A., Nilsson, B.J. (eds) Fundamentals of Computation Theory. FCT 2003. Lecture Notes in Computer Science, vol 2751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45077-1_22

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  • DOI: https://doi.org/10.1007/978-3-540-45077-1_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40543-6

  • Online ISBN: 978-3-540-45077-1

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