Skip to main content
SpringerLink
Log in

Improved Minmax Regret 1-Center Algorithms for Cactus Networks with c Cycles

  • Conference paper
Book cover LATIN 2014: Theoretical Informatics (LATIN 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8392))

Included in the following conference series:

Abstract

In a facility location problem, if the vertex weights are uncertain one may look for a “robust” solution that minimizes “regret.” We present an O(nlogn) (resp. O(cnlogn)) time algorithm for a tree (resp. c-cycle cactus), where n is the number of vertices and c is a constant. Our tree algorithm presents an improvement over the previously known algorithms that run in O(nlog2 n) time. There is no previously published result tailored specifically for a cactus network. The best algorithm for a general network takes O(mn logn) time, where m is the number of edges.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Averbakh, I.: Complexity of robust single-facility location problems on networks with uncertain lengths of edges. Disc. Appl. Math. 127, 505–522 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Averbakh, I., Berman, O.: Minimax regret p-center location on a network with demand uncertainty. Location Science 5, 247–254 (1997)

    Article  MATH  Google Scholar 

  3. Averbakh, I., Berman, O.: Algorithms for the robust 1-center problem on a tree. European Journal of Operational Research 123(2), 292–302 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ben-Moshe, B., Bhattacharya, B., Shi, Q., Tamir, A.: Efficient algorithms for center problems in cactus networks. Theoretical Compter Science 378(3), 237–252 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Benkoczi, R.: Cardinality constrained facility location problems in trees. Ph.D. thesis, School of Computing Science, Simon Fraser University, Canada (2004)

    Google Scholar 

  6. Benkoczi, R., Bhattacharya, B., Chrobak, M., Larmore, L.L., Rytter, W.: Faster algorithms for k-medians in trees. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 218–227. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Bhattacharya, B., Kameda, T., Song, Z.: Minmax regret 1-center on a path/cycle/tree. In: Proc. 6th Int’l Conf. on Advanced Engineering Computing and Applications in Sciences (ADVCOMP), pp. 108–113 (2012), http://www.thinkmind.org/index.php?view=article&articleid=advcomp_2012_5_20_20093

  8. Burkard, R., Dollani, H.: A note on the robust 1-center problem on trees. Annals of Operational Research 110, 69–82 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Burkard, R., Krarup, J.: A linear algorithm for the pos/neg-weighted 1-median problem on a cactus. Computing 60, 193–215 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  10. Chazelle, B., Guibas, L.J.: Fractional cascading: II. Applications. Algorithmica 1, 163–191 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  11. Chen, B., Lin, C.S.: Minmax-regret robust 1-median location on a tree. Networks 31, 93–103 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Goldman, A.: Optimal center location in simple networks. Transportation Science 5, 212–221 (1971)

    Article  MathSciNet  Google Scholar 

  13. Hakimi, S.: Optimum locations of switching centers and the absolute centers and medians of a graph. Operations Research 12, 450–459 (1964)

    Article  MATH  Google Scholar 

  14. Hale, T.S., Moberg, C.R.: Location science research: A review. Annals of Operations Research 123, 21–35 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kouvelis, P., Vairaktarakis, G., Yu, G.: Robust 1-median location on a tree in the presence of demand and transportation cost uncertainty. Tech. Rep. Working Paper 93/94-3-4, Department of Management Science, The University of Texas, Austin (1993)

    Google Scholar 

  16. Megiddo, N.: Linear-time algorithms for linear-programming in R 3 and related problems. SIAM J. Computing 12, 759–776 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  17. Megiddo, N., Tamir, A.: New results on the complexity of p-center problems. SIAM J. Computing 12, 751–758 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  18. Tamir, A.: An O(pn 2) algorithm for the p-median and the related problems in tree graphs. Operations Research Letters 19, 59–64 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  19. Yu, H.I., Lin, T.C., Wang, B.F.: Improved algorithms for the minmax-regret 1-center and 1-median problem. ACM Transactions on Algorithms 4(3), 1–1 (2008)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computing Science, Simon Fraser University, Canada

    Binay Bhattacharya & Tsunehiko Kameda

  2. Department of Computer Science, The University of Texas at Austin, USA

    Zhao Song

Authors
  1. Binay Bhattacharya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tsunehiko Kameda
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhao Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Facultad de Ingeniería, Instituto de Computación, Universidad de la República, Julio Herrera y Reissig 565, 11300, Montevideo, Uruguay

    Alberto Pardo  & Alfredo Viola  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bhattacharya, B., Kameda, T., Song, Z. (2014). Improved Minmax Regret 1-Center Algorithms for Cactus Networks with c Cycles. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-54423-1_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54422-4

  • Online ISBN: 978-3-642-54423-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation