Skip to main content
Springer Nature Link
Log in

A Primal Dual Approximation Algorithm for the Multicut Problem in Trees with Submodular Penalties

  • Conference paper
  • First Online:
Algorithmic Aspects in Information and Management (AAIM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11640))

Included in the following conference series:

Abstract

In this paper, we introduce the multicut problem in trees with submodular penalties, which generalizes the prize-collecting multicut problem in trees and vertex cover with submodular penalties. We present a combinatorial 3-approximation algorithm, based on the primal-dual scheme for the multicut problem in trees.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. Dahlhaus, E., Johnson, D.S., Papadimitriou, C.H., Seymour, P.D., Yannakakis, M.: The complexity of multiterminal cuts. SIAM J. Comput. 23(4), 864–894 (1994)

    Article  MathSciNet  Google Scholar 

  2. Du, D., Lu, R., Xu, D.: A primal-dual approximation algorithm for the facility location problem with submodular penalties. Algorithmica 63, 191–200 (2012)

    Article  MathSciNet  Google Scholar 

  3. Fujishige, S.: Submodular Functions and Optimization, 2nd edn. Elsevier, Amsterdam (2005)

    MATH  Google Scholar 

  4. Garg, N., Vazirani, V.V., Yannakakis, M.: Approximate max-flow min-(multi) cut theorems and their applications. SIAM J. Comput. 25(2), 235–251 (2006)

    Article  MathSciNet  Google Scholar 

  5. Garg, N., Vazirani, V.V., Yannakakis, M.: Primal-dual approximation algorithms for integral flow and multicut in trees. Algorithmica 18(1), 3–20 (1997)

    Article  MathSciNet  Google Scholar 

  6. Hayrapetyan, A., Swamy, C., Tardos, E.: Network design for information networks. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 933–942 (2005)

    Google Scholar 

  7. Hu, T.C.: Integer Programming and Network Flows. Addison-Wesley, Reading (1969)

    MATH  Google Scholar 

  8. Iwata, S., Fleischer, L., Fujishige, S.: A combinatorial strongly polynomial algorithm for minimizing submodular functions. J. ACM 48(4), 761–777 (2001)

    Article  MathSciNet  Google Scholar 

  9. Iwata, S., Nagano, K.: Submodular function minimization under covering constraints. In: The 50th Annual Symposium on Foundations of Computer Science, FOCS, pp. 671–680 (2009)

    Google Scholar 

  10. Kamiyama, N.: A note on the submodular vertex cover problem withsubmodular penalties. Theor. Comput. Sci. 659, 95–97 (2017)

    Article  Google Scholar 

  11. Kanj, I., et al.: Improved parameterized and exact algorithms for cut problems on trees. Theor. Comput. Sci. 607, 455–470 (2015)

    Article  MathSciNet  Google Scholar 

  12. Khot, S., Regev, O.: Vertex cover might be hard to approximateto with \(2-\epsilon \). J. Comput. Syst. Sci. 74(3), 335–349 (2008)

    Article  Google Scholar 

  13. Levin, A., Segev, D.: Partial multicuts in trees. Theor. Comput. Sci. 369(1–3), 384–395 (2006)

    Article  MathSciNet  Google Scholar 

  14. Li, Y., Du, D., Xiu, N., Xu, D.: Improved approximation algorithms for the facility location problems with linear/submodular penalties. Algorithmica 73(2), 460–482 (2015)

    Article  MathSciNet  Google Scholar 

  15. Liu, H., Zhang, P.: On the generalized multiway cut in trees problem. J. Comb. Optim. 27(1), 65–77 (2014)

    Article  MathSciNet  Google Scholar 

  16. Xu, D., Wang, F., Du, D., Wu, C.: Approximation algorithms for submodular vertex cover problems with linear/submodular penalties using primal-dual technique. Theor. Comput. Sci. 630, 117–125 (2016)

    Article  MathSciNet  Google Scholar 

  17. Zhang, P., Zhu, D., Luan, J.: An approximation algorithm for the generalized k-multicut problem. Discrete Appl. Math. 160(7–8), 1240–1247 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The work is supported in part by the National Natural Science Foundation of China [No. 61662088], Program for Excellent Young Talents of Yunnan University, Training Program of National Science Fund for Distinguished Young Scholars, IRTSTYN, and Key Joint Project of the Science and Technology Department of Yunnan Province and Yunnan University [No. 2018FY001(-014)].

Author information

Authors and Affiliations

  1. School of Electronic Engineering and Computer Science, Peking University, Beijing, 100871, People’s Republic of China

    Xiaofei Liu

  2. School of Mathematics and Statistics, Yunnan University, Kunming, 650504, People’s Republic of China

    Weidong Li

  3. Dianchi College of Yunnan University, Kunming, 650000, People’s Republic of China

    Weidong Li

Authors
  1. Xiaofei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weidong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Weidong Li .

Editor information

Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. Hefei University of Technology, Hefei, China

    Lian Li

  3. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Xiaoming Sun

  4. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Jialin Zhang

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Liu, X., Li, W. (2019). A Primal Dual Approximation Algorithm for the Multicut Problem in Trees with Submodular Penalties. In: Du, DZ., Li, L., Sun, X., Zhang, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2019. Lecture Notes in Computer Science(), vol 11640. Springer, Cham. https://doi.org/10.1007/978-3-030-27195-4_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-27195-4_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-27194-7

  • Online ISBN: 978-3-030-27195-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation