Advertisement

Searching Rectilinear Streets Completely

  • Christoph A. Bröcker
  • Sven Schuierer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1663)

Abstract

We consider the on-line navigation problem of a robot inside an unknown polygon P. The robot has to find a path from a starting point to an unknown goal point and it is equipped with on-board cameras through which it can get the visibility map of its immediate surroundings. It is known that if P is a street with respect to two points s and t then starting at s the robot can find t with a constant competitive ratio. In this paper we consider the case where the robot is inside a rectilinear street but looks for an arbitrary goal point g instead of t. Furthermore, it may start at some point different from s. We show that in both cases a constant competitive ratio can be achieved and establish lower bounds for this ratio. If the robot starts at s, then our lower and upper bound match, that is, our algorithm is optimal.

Keywords

Search Direction Competitive Ratio Simple Polygon Competitive Strategy Search Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BBF+96]
    P. Berman, A. Blum, A. Fiat, H. Karloff, A. Rosén, and M. Saks. Randomized robot navigation algorithms. In Proc. 7th ACM-SIAM Symp. On Discrete Algorithms, 1996.Google Scholar
  2. [BBFY94]
    E. Bar-Eli, P. Berman, A. Fiat, and P. Yan. Online navigation in a room. J. Algorithms, 17:319–341, 1994.MathSciNetCrossRefGoogle Scholar
  3. [BRS91]
    A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrain. In Proc. 23rd ACM Sympos. Theory Comput., pages 494–503, 1991.Google Scholar
  4. [BYCR93]
    R. A. Baeza-Yates, J. C. Culberson, and G. J. Rawlins. Searching in the plane. Information and Computation, 106:234–252, 1993.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [CL93]
    K-F. Chan and T. W. Lam. An on-line algorithm for navigating in an unknown environment. Computational Geometry: Theory and Applications, 3:227–244, 1993.MathSciNetzbMATHGoogle Scholar
  6. [DHS95]
    A. Datta, Ch. Hipke, and S. Schuierer. Competitive searching in polygons-beyond generalized streets. In J. Staples, P. Eades, N. Katoh, and A. Moffat, editors, Proc. Sixth Annual International Symposium on Algorithms and Computation, pages 32–41. LNCS 1004, 1995.Google Scholar
  7. [DI94]
    A. Datta and Ch. Icking. Competitive searching in a generalized street. In Proc. of the 10th Annual ACM Symp. on Computational Geometry, pages 175–182, 1994.Google Scholar
  8. [DKP98]
    X. Deng, T. Kameda, and C. Papadimitriou. How to learn an unknown environment I: The rectilinear case. J. of the ACM, 45(2):215–245, 1998.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [ELW93]
    P. Eades, X. Lin, and N. C. Wormald. Performance guarantees for motion planning with temporal uncertainty. The Australian Computer Journal, 25(1):21–28, 1993.Google Scholar
  10. [Gal80]
    S. Gal. Search Games. Academic Press, 1980.Google Scholar
  11. [IKL99]
    Ch. Icking, R. Klein, and E. Langetepe. An optimal competitive strategy for walking in streets. In Proc. 16th Annual Symposium on Theoretical Aspects of Computer Science, pages 110–120, LNCS 1563, 1999.Google Scholar
  12. [Kle91]
    R. Klein. Walking an unknown street with bounded detour. In Proc. 32nd IEEE Symp. On Foundations of Computer Science, pages 304–313, 1991.Google Scholar
  13. [Kle94]
    J. M. Kleinberg. On-line search in a simple polygon. In Proc. 5th ACM-SIAM Symp. on Discrete Algorithms, pages 8–15, 1994.Google Scholar
  14. [KP93]
    B. Kalyanasundaram and K. Pruhs. A competitive analysis of algorithms for searching unknown scenes. Computational Geometry: Theory and Applications, 3:139–155, 1993.MathSciNetzbMATHCrossRefGoogle Scholar
  15. [LOS97]
    A. López-Ortiz and S. Schuierer. Position-independent near optimal searching and on line recognition in star polygons. In Proc. 5th Workshop on Algorithms and Data Structures, pages 284–296. LNCS 1272, 1997.CrossRefGoogle Scholar
  16. [MI94]
    A. Mei and Y. Igarashi. An efficiency strategy for robot navigation in unknown environment. Information Processing Letters, 52(1):51–56, 1994.CrossRefGoogle Scholar
  17. [PY91]
    C. H. Papadimitriou and M. Yannakakis. Shortest paths without a map. Theoretical Computer Science, 84(1):127–150, 1991.MathSciNetzbMATHCrossRefGoogle Scholar
  18. [Sch97]
    S. Schuierer. On-line searching in geometric trees. In Proc. 9th Canadian Conf. On Computational Geometry, pages 135–140, 1997.Google Scholar
  19. [SS99]
    S. Schuierer and I. Semrau. An optimal strategy for searching in unknown streets. In Proc. 16th Annual Symposium on Theoretical Aspects of Computer Science, pages 121–131, LNCS 1563, 1999.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Christoph A. Bröcker
    • 1
  • Sven Schuierer
    • 1
  1. 1.Institut für InformatikUniversitäat FreiburgFreiburgGermany

Personalised recommendations