Skip to main content
SpringerLink
Log in

Simplifying Flow Networks

  • Conference paper
  • First Online:
Book cover Mathematical Foundations of Computer Science 2000 (MFCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1893))

Abstract

Maximum flow problems appear in many practical applications. In this paper, we study how to simplify a given directed flow network by finding edges that can be removed without changing the value of the maximum flow. We give a number of approaches which are increasingly more complex and more time-consuming, but in exchange they remove more and more edges from the network.

Supported by NSERC Research Grant.

Supported by NSERC Research Grant OGP0046506 and ICR Doctoral Scholarship.

Supported by NSERC Research Grant OGP0046506.

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 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. Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin. Network Flows: Theory, Algorithms and Applications. Prentice Hall, 1993.

    Google Scholar 

  2. Therese Biedl, Broňa Brejová, and Tomáš Vinař. Simplifying flow networks. Technical Report CS-2000-07, Department of Computer Science, University of Waterloo, 2000.

    Google Scholar 

  3. Steven Fortune, John Hopcroft, and James Wyllie. The directed subgraph homeomorphism problem. Theoretical Computer Science, 10(2):111–121, February 1980.

    Google Scholar 

  4. Donald B. Johnson and Shankar M. Venkatesan. Using divide and conquer to find flows in directed planar networks in O(n3/2 log n) time. In Proceedings of the 20th Annual Allerton Conference on Communication, Control, and Computing, pages 898–905, University of Illinois, Urbana-Champaign, 1982.

    Google Scholar 

  5. Samir Khuller, Joseph Naor, and Philip Klein. The lattice structure of flow in planar graphs. SIAM Journal on Discrete Mathematics, 6(3):477–490, August 1993.

    Google Scholar 

  6. Franco P. Preparata and Micheal I. Shamos. Computational Geometry: An Introduction. Springer-Verlag, 1985.

    Google Scholar 

  7. Alexander Schrijver. Finding k disjoint paths in a directed planar graph. SIAM Journal of Computing, 23(4):780–788, August 1994.

    Google Scholar 

  8. Daniel D. Sleator and Robert E. Tarjan. A data structure for dynamic trees. Journal of Computer and System Sciences, 26(3):362–391, June 1983.

    Google Scholar 

  9. Karsten Weihe. Maximum (s, t)-flows in planar networks in O(¦V¦ log ¦V¦) time. Journal of Computer and System Sciences, 55(3):454–475, December 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Waterloo, USA

    Therese C. Biedl, Broňa Brejová & Tomáš Vinař

Authors
  1. Therese C. Biedl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Broňa Brejová
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tomáš Vinař
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, 8000, Aarhus C, Denmark

    Mogens Nielsen

  2. Department of Computer Sciene, Comenius University, 84248, Bratislava, Slovakia

    Branislav Rovan

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Biedl, T.C., Brejová, B., Vinař, T. (2000). Simplifying Flow Networks. In: Nielsen, M., Rovan, B. (eds) Mathematical Foundations of Computer Science 2000. MFCS 2000. Lecture Notes in Computer Science, vol 1893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44612-5_15

Download citation

  • DOI: https://doi.org/10.1007/3-540-44612-5_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67901-1

  • Online ISBN: 978-3-540-44612-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation