Skip to main content

Line Segment Facility Location in Weighted Subdivisions

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 5564))

Abstract

In this paper we present approximation algorithms for solving the line segment facility location problem in weighted regions. The weighted region setup is a more realistic model for many facility location problems that arise in practical applications. Our algorithms exploit an interesting property of the problem, that could possibly be used for solving other problems in weighted regions.

This research was partially supported by NSF grant CCF-0635013.

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

Buying options

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 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aleksandrov, L., Djidjev, H.N., Guo, H., Maheshwari, A., Nussbaum, D., Sack, J.R.: Algorithms for approximate shortest path Queries on weighted polyhedral surfaces. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 98–109. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  2. Aleksandrov, L., Maheshwari, A.A., Sack, J.R.: Approximation algorithms for geometric shortest path problems. In: Proc. 32nd Annual ACM Symposium on Theory of Computing, pp. 286–295 (2000)

    Google Scholar 

  3. Aleksandrov, L., Maheshwari, A., Sack, J.R.: Determining approximate shortest paths on weighted polyhedral surfaces. Journal of the ACM 52(1), 25–53 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Amato, N.M., Goodrich, M.T., Ramos, E.A.: Computing the arrangement of curve segments: Divide-and-conquer algorithms via sampling. In: Proc. 11th Annual CAM-SIAM Symposium on Discrete Algorithms, pp. 705–706 (2000)

    Google Scholar 

  5. Chen, D.Z., Daescu, O., Hu, X., Wu, X., Xu, J.: Determining an optimal penetration among weighted regions in two and three dimensions. Journal of Combinatorial Optimization 5(1), 59–79 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chen, D.Z., Hu, X., Xu, J.: Computing Optimal Beams in Two and Three Dimensions. Journal of Combinatorial Optimization 7(2), 111–136 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cheng, S.W., Na, H.S., Vigneron, A., Wang, Y.: Approximate shortest paths in anisotropic regions. SIAM Journal on Computing 38, 802–824 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Cheng, S.W., Na, H.S., Vigneron, A., Wang, Y.: Querying approximate shortest paths in anisotropic regions. In: Proc. 23rd Symposium on Computational Geometry, pp. 84–91 (2007)

    Google Scholar 

  9. Cheung, Y., Daescu, O.: Line Facility Location in Weighted Regions. In: Proc. 4th Intl. Conf. on Algorithmic Aspects in Information and Management, pp. 109–119 (2008)

    Google Scholar 

  10. Daescu, O.: Improved optimal weighted links algorithms. In: Proc. ICCS, 2nd International Workshop on Computational Geometry and Applications, pp. 227–233 (2002)

    Google Scholar 

  11. Daescu, O., Palmer, J.: Minimum Separation in Weighted Subdivisions. International Journal of Computational Geometry and Applications 19(1), 33–57 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  12. Imai, H., Kato, K., Yamamoto, P.: A linear-time algorithm for linear L 1 approximation of points. Algorithmica 4(1), 77–96 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  13. Goemans, M.X., Skutella, M.: Cooperative facility location games. Journal of Algorithms 50(2), 194–214 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Megiddo, N., Tamir, A.: Finding Least-Distance Lines. SIAM Journal of Algebraic Discrete Methods 4(2), 207–211 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  15. Mitchell, J.S.B., Papdimitriou, C.H.: The weighted region problem: Finding shortest paths through a weighted planer subdivision. Journal of the ACM 38(1), 18–73 (1991)

    Article  Google Scholar 

  16. Preparata, F.P., Shamos, M.I.: Computational Geometry: An Introduction. Springer, New York (1985)

    Book  MATH  Google Scholar 

  17. Sun, Z., Reif, J.H.: On finding approximate optimal path in weighted regions. Journal of Algorithms 58(1), 1–32 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  18. Toussaint, G.T.: Solving geometric problems with the rotating calipers. In: Proc. 2nd IEEE Mediterranean Electrotechnical Conference (MELECON 1983), pp. 1–4 (1983)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cheung, Y.K., Daescu, O. (2009). Line Segment Facility Location in Weighted Subdivisions. In: Goldberg, A.V., Zhou, Y. (eds) Algorithmic Aspects in Information and Management. AAIM 2009. Lecture Notes in Computer Science, vol 5564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02158-9_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02158-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02157-2

  • Online ISBN: 978-3-642-02158-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics