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Position-Independent Street Searching

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Algorithms and Data Structures (WADS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1663))

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Abstract

A polygon P is a street if there exist points (u,v) on the boundary such that P is weakly visible from any path from u to v. Optimal strategies have been found for on-line searching of streets provided that the starting position of the robot is s = u and the target is located at t = v. Thus a hiding target could foil the strategy of the robot by choosing its position t in such a manner as not to realize a street. In this paper we introduce a strategy with a constant competitive ratio to search a street polygon for a target located at an arbitrary point t on the boundary, starting at any other arbitrary point s on the boundary. We also provide lower bounds for this problem. This makes streets only the second non-trivial class of polygons (after stars) known to admit a constant-competitive-ratio strategy in the general position case.

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References

  1. R. Baeza-Yates, J. Culberson and G. Rawlins. “Searching in the plane”, Information and Computation, Vol. 106, (1993), pp. 234–252.

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Beck. “On the linear search problem”, Israel Journal of Mathematics, Vol. 2,(1964), pp. 221–228.

    Article  MathSciNet  MATH  Google Scholar 

  3. B. Bhattacharya and S. K. Ghosh, “Characterizing LR-visibility polygons and related problems”, Proc. 10th Canadian Conference on Comp. Geom., (1998).

    Google Scholar 

  4. C. A. Bröcker and S. Schuierer, “Searching Rectilinear Streets Completely”, In these Proceedings.

    Google Scholar 

  5. A. Datta, Ch. Hipke, and S. Schuierer. “Competitive searching in polygons-beyond generalized streets”, in Proc. 6th Int. Symposium on Algorithms and Computation (ISAAC), pages 32–41. LNCS 1004, 1995.

    Google Scholar 

  6. A. Datta and Ch. Icking. “Competitive searching in a generalized street”, Proceedings 10th ACM Symposium on Computational Geometry (SoCG), (1994), pp. 175–182.

    Google Scholar 

  7. S. Gal. Search Games, Academic Press, 1980.

    Google Scholar 

  8. Ch. Icking. “Motion and visibility in simple polygons.” Ph.D. Thesis, Fernuniversität Hagen, 1994.

    Google Scholar 

  9. Ch. Icking and R. Klein. “Searching for the kernel of a polygon. A competitive Strategy”, Proc. 11th ACM Symposium on Computational Geometry (SoCG), (1995).

    Google Scholar 

  10. Ch. Icking, R. Klein and E. Langetepe. “An Optimal Competitive Strategy for Walking in Streets.” Tech.Rep. 233, Dept. of Comp. Sci., FernUniversität Hagen, Germany, 1998.

    Google Scholar 

  11. B. Kalyasundaram and K. Pruhs. “A competitive analysis of algorithms for searching unknown scenes”, Comp. Geom.: Theory and Applications, Vol. 3, (1993), pp. 139–155.

    Article  Google Scholar 

  12. M.-Y. Kao, J. H. Reif and S. R. Tate. “Searching in an unknown environment: An optimal randomized algorithm for the cow-path problem”, Proceedings of 4th ACM-SIAM Symposium on Discrete Algorithms (SODA), (1993), pp. 441–447.

    Google Scholar 

  13. R. Klein. “Walking an unknown street with bounded detour”, Comp. Geom.: Theory and Applications, Vol. 1, (1992), pp. 325–351, also in 32nd FOCS, 1991.

    Article  MATH  Google Scholar 

  14. J. Kleinberg. “On-line search in a simple polygon”, Proceedings of 5th ACM-SIAM Symposium on Discrete Algorithms (SODA), (1994), pp. 8–15.

    Google Scholar 

  15. A. López-Ortiz. “On-line target searching in bounded and unbounded domains”, Ph.D. thesis, University of Waterloo, 1996.

    Google Scholar 

  16. A. López-Ortiz and S. Schuierer. “Going home through an unknown street”, Proc. 4th Workshop on Data Structures and Algorithms (WADS), 1995, Lecture Notes in Computer Science 955, Springer-Verlag, pp. 135–146.

    Google Scholar 

  17. A. López-Ortiz and S. Schuierer. “Generalized streets revisited”, In J. Diaz and M. Serna, editors, Proc. 4th European Symposium on Algorithms (ESA), LNCS 1136, pages 546–558. Springer Verlag, 1996.

    Google Scholar 

  18. A. López-Ortiz and S. Schuierer. “Walking streets faster”, Proc. 5th Scandina-vian Workshop in Algorithmic Theory Algorithms (SWAT), 1996, Lecture Notes in Computer Science 1097, Springer-Verlag, pp. 345–356.

    Google Scholar 

  19. A. López-Ortiz and S. Schuierer. “Position-independent Near Optimal Searching and On-line Recognition in Star Polygons”, Proc. 5th Workshop on Algorithms and Data Structures (WADS), (1997), Lecture Notes in Computer Science, pp. 284–296.

    Google Scholar 

  20. S. Schuierer and I. Semrau. “An optimal strategy for searching in unknown streets.” Proc. 16th Symp. on Theoretical Aspects of Computer Science, to appear, 1999

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Freiburg, Am Flughafen 17, Geb. 051, D-79110, Freiburg, FRG

    Christoph A. Bröcker

  2. Faculty of Computer Science, University of New Brunswick, Fredericton, New Brunswick, Canada, E3B 4A1

    Alejandro López-Ortiz

Authors
  1. Christoph A. Bröcker
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  2. Alejandro López-Ortiz
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Canada, K1S 5B6

    Frank Dehne  & Jörg-Rüdiger Sack  & 

  2. School of Computer Science, Simon Fraser University, Burnaby, BC, Canada, V5A 1S6

    Arvind Gupta

  3. Center for Geometric Computing Providence, Brown University, RI, 02912-1910, USA

    Roberto Tamassia

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© 1999 Springer-Verlag Berlin Heidelberg

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Bröcker, C.A., López-Ortiz, A. (1999). Position-Independent Street Searching. In: Dehne, F., Sack, JR., Gupta, A., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1999. Lecture Notes in Computer Science, vol 1663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48447-7_25

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  • DOI: https://doi.org/10.1007/3-540-48447-7_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66279-2

  • Online ISBN: 978-3-540-48447-9

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