Skip to main content
SpringerLink
Log in

An Improved On-line Strategy for Exploring Unknown Polygons

  • Conference paper
  • First Online:
Combinatorial Optimization and Applications

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9486))

Abstract

We present a new, on-line strategy for a mobile robot to explore an unknown simple polygon P, so as to output a so-called watchman route such that every interior point of P is visible from at least one point along the route. The length of the robot?s route is guaranteed to be at most 6.7 times that of the shortest watchman route that could be computed off-line. This significantly improves upon the previously known 26.5-competitive strategy. A novelty of our strategy is an on-line implementation of a previously known off-line algorithm that approximates the optimum watchman route to a factor of \(\sqrt{2}\). The other is in the way the polygon exploration problem is decomposed into two different types of the subproblems and a new method for analyzing its cost performance.

This work was supported by JSPS KAKENHI Grant Number 15K00023.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

References

  1. Chin, W.P., Ntafos, S.: Optimum watchman routes. IPL 28, 39?44 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  2. Deng, X., Kameda, T., Papadimitriou, C.: How to learn an unknown environment. In: Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, pp. 298?303 (1991)

    Google Scholar 

  3. Dror, M., Efrat, A., Lubiw, A., Mitchell, J.S.B.: Touring a sequence of simple polygons. In: Proceedings of the 35th Annual ACM Symposium Theory of Computing, pp. 473?482 (2003)

    Google Scholar 

  4. Hoffmann, F., Icking, C., Klein, R., Kriegel, K.: The polygon exploration problem. SIAM J. Comput. 31(2), 577?600 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Tan, X.: Approximation algorithms for the watchman and zookeeper’s problems. Discrete Appl. Math. 136, 363?376 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Tan, X., Hirata, T., Inagaki, Y.: An incremental algorithm for constructing shortest watchman routes. Int. J. Comput. Geom. Appl. 3, 351?365 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  7. Tan, X., Hirata, T., Inagaki, Y.: Corrigendum to an incremental algorithm for constructing shortest watchman routes. IJCGA 9, 319?323 (1999)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dalian Maritime University, Linghai Road 1, Dalian, China

    Xuehou Tan & Qi Wei

  2. Tokai University, 4-1-1 Kitakaname, Hiratsuka, 259-1292, Japan

    Xuehou Tan

Authors
  1. Xuehou Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qi Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xuehou Tan .

Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Marywood University, Scranton, Pennsylvania, USA

    Zaixin Lu

  2. North Carolina Central University, Durham, North Carolina, USA

    Donghyun Kim

  3. University of Texas at Dallas, Richardson, Texas, USA

    Weili Wu

  4. Texas Southern University, Houston, Texas, USA

    Wei Li

  5. University of Texas at Dallas, Richardson, Texas, USA

    Ding-Zhu Du

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Tan, X., Wei, Q. (2015). An Improved On-line Strategy for Exploring Unknown Polygons. In: Lu, Z., Kim, D., Wu, W., Li, W., Du, DZ. (eds) Combinatorial Optimization and Applications. Lecture Notes in Computer Science(), vol 9486. Springer, Cham. https://doi.org/10.1007/978-3-319-26626-8_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-26626-8_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26625-1

  • Online ISBN: 978-3-319-26626-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation