Advertisement

The Ultimate Strategy to Search on m Rays?

  • Alejandro López-Ortiz
  • Sven Schuierer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1449)

Abstract

We consider the problem of searching on m current rays for a target of unknown location. If no upper bound on the distance to the target is known in advance, then the optimal competitive ratio is 1 + 2m m/(m − 1)m−1. We show that if an upper bound of D on the distance to the target is known in advance, then the competitive ratio of any searchst rategy is at least 1 + 2m m/(m − 1)m−1O(1/log2 D) which is also optimal—but in a stricter sense.

We also construct a search strategy that achieves this ratio. Astonishingly, our strategy works equally well for the unbounded case, that is, if the target is found at distance D from the starting point, then the competitive ratio is 1 + 2m m/(m − 1)m−1O(1/log2 D) and it is not necessary for our strategy to know an upper bound on D in advance.

Keywords

Search Strategy Optimal Strategy Recurrence Equation Competitive Ratio Positive Real Root 
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. 1.
    R. Baeza-Yates, J. Culberson, and G. Rawlins. Searching in the plane. Information and Computation, 106:234–252, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    A. Datta, Ch. Hipke, and S. Schuierer. Competitive searching in polygons—beyond generalized streets. In Proc. Sixth Annual International Symposium on Algorithms and Computation, pages 32–41. LNCS 1004, 1995.Google Scholar
  3. 3.
    A. Datta and Ch. Icking. Competitive searching in a generalized street. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 175–182, 1994.Google Scholar
  4. 4.
    S. Gal. Search Games. Academic Press, 1980.Google Scholar
  5. 5.
    Ch. Hipke. Online-Algorithmen zur kompetitiven Suche in einfachen Polygonen. Master’s thesis, Universität Freiburg, 1994.Google Scholar
  6. 6.
    Ch. Icking and R. Klein. Searching for the kernel of a polygon: A competitive strategy. In Proc. 11th Annu. ACM Sympos. Comput. Geom., pages 258–266, 1995.Google Scholar
  7. 7.
    Ch. Icking, R. Klein, and E. Langetepe. How to find a point on a line within a fixed distance. Informatik-Bericht 220, Fernuni Hagen, November 1997.Google Scholar
  8. 8.
    M.-Y. Kao, Y. Ma, M. Sipser, and Y. Yin. Optimal constructions of hybrid algorithms. In Proc. 5th ACM-SIAM Sympos. Discrete Algorithms, pages 372–381, 1994.Google Scholar
  9. 9.
    M.-Y. Kao, J. H. Reif, and S. R. Tate. Searching in an unknown environment: An optimal randomized algorithm for the cow-path problem. In Proc. 4th ACM-SIAM Sympos. Discrete Algorithms, pages 441–447, 1993.Google Scholar
  10. 10.
    R. Klein. Walking an unknown street withb ounded detour. Comput. Geom. Theory Appl., 1:325–351, 1992.zbMATHGoogle Scholar
  11. 11.
    R. Klein. Algorithmische Geometrie. Addison-Wesley, 1997.Google Scholar
  12. 12.
    E. Koutsoupias, Ch. Papadimitriou, and M. Yannakakis. Searching a fixed graph. In Proc. 23rd Intern. Colloq. on Automata, Languages and Programming, pages 280–289. LNCS 1099, 1996.Google Scholar
  13. 13.
    A. López-Ortiz. On-line Searching on Bounded and Unbounded Domains. Ph D thesis, Department of Computer Science, University of Waterloo, 1996.Google Scholar
  14. 14.
    A. López-Ortiz and S. Schuierer. Going home through an unknown street. In S. G. Akl, F. Dehne, and J.-R. Sack, editors, Proc. 4th Workshop on Algorithms and Data Structures, pages 135–146. LNCS 955, 1995.Google Scholar
  15. 15.
    A. López-Ortiz and S. Schuierer. Generalized streets revisited. In M. Serna, J. Diaz, editor, Proc. 4th European Symposium on Algorithms, pages 546–558. LNCS 1136, 1996.Google Scholar
  16. 16.
    A. López-Ortiz and S. Schuierer. Position-independent near optimal searching and on-line recognition in star polygons. In Proc. 4th Workshop on Algorithms and Data Structures, pages 284–296. LNCS 1272, 1997.Google Scholar
  17. 17.
    C. H. Papadimitriou and M. Yannakakis. Shortest paths without a map. In Proc. 16th Internat. Colloq. Automata Lang. Program., pages 610–620. LNCS 372, 1989.CrossRefGoogle Scholar
  18. 18.
    D. D. Sleator and R. E. Tarjan. Amortized efficiency of list update and paging rules. Communications of the ACM, 28:202–208, 1985.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Alejandro López-Ortiz
    • 1
  • Sven Schuierer
    • 2
  1. 1.Faculty of Computer ScienceUniversity of New BrunswickCanada
  2. 2.Institut für InformatikUniversität FreiburgFreiburgFRG

Personalised recommendations