Skip to main content

Competitive Online Approximation of the Optimal Search Ratio

  • Conference paper
Algorithms – ESA 2004 (ESA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3221))

Included in the following conference series:

Abstract

How efficiently can we search an unknown environment for a goal in unknown position? How much would it help if the environment were known? We answer these questions for simple polygons and for general graphs, by providing online search strategies that are as good as the best offline search algorithms, up to a constant factor. For other settings we prove that no such online algorithms exist.

The work described in this paper was partially supported by a grant from the Germany/Hong Kong Joint Research Scheme sponsored by the Research Grants Council of Hong Kong and the German Academic Exchange Service (Project No. G-HK024/02).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albers, S., Kursawe, K., Schuierer, S.: Exploring unknown environments with obstacles. In: Proc. 10th SODA, pp. 842–843 (1999)

    Google Scholar 

  2. Alpern, S., Gal, S.: The Theory of Search Games and Rendezvous. Kluwer Academic Publications, Dordrecht (2002)

    Google Scholar 

  3. Baeza-Yates, R., Culberson, J., Rawlins, G.: Searching in the plane. Inform. Comput. 106, 234–252 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  4. Berman, P.: On-line searching and navigation. In: Fiat, A., Woeginger, G. (eds.) Competitive Analysis of Algorithms, Springer, Heidelberg (1998)

    Google Scholar 

  5. Chin, W.-P., Ntafos, S.: Shortest watchman routes in simple polygons. Discrete Comput. Geom. 6(1), 9–31 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  6. Deng, X., Kameda, T., Papadimitriou, C.: How to learn an unknown environment I: The rectilinear case. Journal of the ACM 45(2), 215–245 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Deng, X., Papadimitriou, C.H.: Exploring an unknown graph. Journal of Graph Theory 32, 265–297 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Dror, M., Efrat, A., Lubiw, A., Mitchell, J.S.B.: Touring a sequence of polygons. In: Proc. 35th STOC, pp. 473–482 (2003)

    Google Scholar 

  9. Duncan, C.A., Kobourov, S.G., Anil Kumar, V.S.: Optimal constrained graph exploration. In: Proc. 12th SODA, pp. 307–314 (2001)

    Google Scholar 

  10. Fleischer, R., Romanik, K., Schuierer, S., Trippen, G.: Optimal robot localization in trees. Information and Computation 171, 224–247 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  11. Hoffmann, F., Icking, C., Klein, R., Kriegel, K.: The polygon exploration problem. SIAM Journal on Computing 31, 577–600 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Icking, C., Klein, R., Langetepe, E.: An optimal competitive strategy for walking in streets. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 110–120. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  13. Klein, R.: Algorithmische Geometrie. Addison-Wesley Longman, Amsterdam (1997)

    MATH  Google Scholar 

  14. Koutsoupias, E., Papadimitriou, C.H., Yannakakis, M.: Searching a fixed graph. In: Meyer auf der Heide, F., Monien, B. (eds.) ICALP 1996. LNCS, vol. 1099, pp. 280–289. Springer, Heidelberg (1996)

    Google Scholar 

  15. Schuierer, S.: On-line searching in simple polygons. In: Christensen, H., Bunke, H., Noltemeier, H. (eds.) Dagstuhl Seminar 1998. LNCS (LNAI), vol. 1724, pp. 220–239. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  16. Schuierer, S., Semrau, I.: An optimal strategy for searching in unknown streets. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 121–131. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  17. Tan, X., Hirata, T., Inagaki, Y.: Corrigendum to “an incremental algorithm for constructing shortest watchman routes”. Internat. J. Comput. Geom. Appl. 9(3), 319–323 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  18. Tan, X.H., Hirata, T., Inagaki, Y.: An incremental algorithm for constructing shortest watchman routes. Internat. J. Comput. Geom. Appl. 3(4), 351–365 (1993)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fleischer, R., Kamphans, T., Klein, R., Langetepe, E., Trippen, G. (2004). Competitive Online Approximation of the Optimal Search Ratio. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30140-0_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23025-0

  • Online ISBN: 978-3-540-30140-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics