Skip to main content
SpringerLink
Log in

Enumerating Near-Min S-T Cuts

  • Chapter
Network Interdiction and Stochastic Integer Programming

Part of the book series: Operations Research/Computer Science Interfaces Series ((ORCS,volume 22))

Abstract

We develop a factoring (partitioning) algorithm for enumerating near-minimum-weight s-t cuts in directed and undirected graphs, with application to network interdiction. “Near-minimum” means within a factor of 1+ε of the minimum for some ε ≥ 0. The algorithm requires only polynomial work per cut enumerated provided that ε is sufficiently (not trivially) small, or G has special structure, e.g., G is a complete graph. Computational results demonstrate good empirical efficiency even for large values of ε and for general graph topologies.

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
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover 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

  • Abel, V., and Bicker, R., (1982), “Determination of All Minimal Cut-Sets between a Vertex Pair in an Undirected Graph,” IEEE Transactions on Reliability, Vol. R-31, pp. 167–171.

    Google Scholar 

  • Ahmad, S.H., (1990), “Enumeration of Minimal Cutsets of an Undirected Graph,” Microelectronics Reliability, Vol. 30, pp. 23–26.

    Google Scholar 

  • Avis, D., and Fukuda, K., (1996) “Reverse Search for Enumeration,” Discrete Applied Mathematics, Vol. 65, pp. 21–46.

    Article  MathSciNet  MATH  Google Scholar 

  • Boyle, M.R., (1998), “Partial-Enumeration For Planar Network Interdiction Problems,” Master’s Thesis, Operations Research Department, Naval Postgraduate School, Monterey, California, March.

    Google Scholar 

  • Bussieck, M.R., and Lübbecke, M.E., (1998), “The Vertex Set of a 0/1-Polytope is Strongly P-enumerable,” Computational Geometry, Vol. 11, pp. 103–109.

    Article  MathSciNet  MATH  Google Scholar 

  • Colbourn, C.J., 1987, The Combinatorics of Network Reliability, Oxford University Press.

    Google Scholar 

  • Curet, N.D., DeVinney, J., Gaston, M.E. 2002, “An Efficient Network Flow Code for Finding All Minimum Cost s-t Cutsets,” Computers and Operations Research, Vol. 29, pp. 205–219.

    Google Scholar 

  • DIMACS, (1991), The First DIMACS International Algorithm Implementation Challenge, Rutgers University, New Brunswick, New Jersey. (Available via anonymous ftp from dimacs.rutgers.edu.)

    Google Scholar 

  • Edmonds, J. and Karp, R.M., (1972), “Theoretical Improvements in Algorithm Efficiency for Network Flow Problems,” Journal of the ACM, Vol. 19, pp. 248–264.

    Article  MATH  Google Scholar 

  • Fard, N.S., and Lee, T.H., (1999), “Cutset Enumeration of Network Systems with Link and Node Failures,” Reliability Engineering and Sys tem Safety, Vol. 65, pp. 141–146.

    Google Scholar 

  • Gibbons, M., (2000), “Enumerating Near-Minimum Cuts in a Network,” Master’s Thesis, Operations Research Department, Naval Postgraduate School, Monterey, California, June.

    Google Scholar 

  • Goldberg, A.V., and Rao, S., (1998), “Beyond the Flow Decomposition Barrier,” Journal of the ACM, Vol. 45, pp. 783–797.

    Article  MathSciNet  MATH  Google Scholar 

  • Goldberg, A.V., and Tarjan, R.E., (1988), “A New Approach to the Maximum Flow Problem,” Journal of the ACM, Vol. 35, pp. 921–940.

    Article  MathSciNet  MATH  Google Scholar 

  • Gusfield, D., and Naor, D., (1993), “Extracting Maximal Information About Sets of Minimum Cuts,” Algorithmica, Vol. 10, pp. 64–89.

    Article  MathSciNet  MATH  Google Scholar 

  • Kanevsky, A., (1993), “Finding All Minimum-Size Separating Vertex Sets in a Graph,” Networks, Vol. 23, pp. 533–541.

    MATH  MathSciNet  Google Scholar 

  • Karger, D.R., (2000), “MinimumCuts in Near-Linear Time,” Journal of the ACM, Vol. 47, pp. 46–76.

    Article  MathSciNet  MATH  Google Scholar 

  • Karger, D.R., and Stein, C, (1996), “A New Approach to the Minimum Cut Problem,” Journal of the ACM, Vol. 43, pp. 601–640.

    Article  MathSciNet  MATH  Google Scholar 

  • Lawler, E.L., Lenstra, J.K., Rinooy Kan, A.H.G., and Shmoys, D.B., (1985), The Traveling Salesman Problem, John Wiley & Sons, Chichester, England.

    MATH  Google Scholar 

  • Levine, M., (1997), “Experimental Study of Minimum Cut Algorithms,” Master’s Thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, May. (http://theory.lcs.mit.edu/~mslevine)

    Google Scholar 

  • Nagamochi, H., Ono, T., and Ibaraki, T., (1994), “Implementing an Efficient Minimum Capacity Cut Algorithm,” Mathematical Programming, Vol. 67, pp. 297–324.

    Article  MathSciNet  Google Scholar 

  • Nagamochi, H., Nishimura, K., and Ibaraki, T., (1997), “Computing All Small Cuts in an Undirected Network,” SIAM Journal on Discrete Mathematics, Vol. 10, pp. 469–481.

    Article  MathSciNet  MATH  Google Scholar 

  • Nahman, J.M., (1997), “Enumeration of Minimal Cuts of Modified Networks,” Microelectronics Reliability, Vol. 37, pp. 483–485.

    Google Scholar 

  • Patvardhan, C, Prasad, V.C. and Pyara, V.P., (1995), “Vertex Cutsets of Undirected Graphs,” IEEE Transactions on Reliability, Vol. 44, pp. 347–353.

    Article  Google Scholar 

  • Picard, J.C., and Queyranne, M., (1980), “On The Structure of All Minimum Cuts in a Network and Applications,” Mathematical Programming Study, Vol. 13, pp. 8–16.

    MathSciNet  MATH  Google Scholar 

  • Prasad, V.C, Sankar, V., and Rao, P., (1992), “Generation of Vertex and Edge Cutsets,” Microelectronics Reliability, Vol. 32, pp. 1291–1310.

    Article  Google Scholar 

  • Provan, J.S., and Ball, M.O., (1983), “Calculating Bounds on Reachability and Connectedness in Stochastic Networks,” Networks, Vol. 13, pp. 253–278.

    MathSciNet  MATH  Google Scholar 

  • Provan, J.S., and Shier, D.R., (1996), “A Paradigm for Listing (s,t)-Cuts in Graphs,” Algorithmica, Vol. 15, pp. 351–372.

    MathSciNet  MATH  Google Scholar 

  • Ramanathan, A., and Colbourn, C.J., (1987), “Counting Almost Minimum Cutsets with Reliability Applications,” Mathematical Programming, Vol. 39, pp. 253–261.

    MathSciNet  MATH  Google Scholar 

  • Shier, D.R., and Whited, D.E., (1986), “Iterative Algorithms for Generating Minimal Cutsets in Directed Graphs,” Networks, Vol. 16, pp. 133–147.

    MathSciNet  MATH  Google Scholar 

  • Sung, C.S., and Yoo, B.K., (1992), “Simple Enumeration of Minimal Cutsets Separating 2 Vertices in a Class of Undirected Planar Graphs,” IEEE Transactions on Reliability, Vol. 41, pp. 63–71.

    Article  MATH  Google Scholar 

  • Sun Microsystems Inc., (1998), Java Platform Version 1.2.2.

    Google Scholar 

  • Tsukiyama, S., Shirakawa, I., Ozaki, H., and Ariyoshi, H., 1980, “An Algorithm to Enumerate All Cutsets of a Graph in Linear Time per Cutset,” Journal of the ACM, Vol. 27, pp. 619–632.

    Google Scholar 

  • Vazirani, V.V., and Yannakakis, M., (1992), “Suboptimal Cuts: Their Enumeration, Weight and Number,” Automata, Languages and Programming. 19th International Colloquium Proceedings, Vol. 623 of Lecture Notes in Computer Science, Springer-Verlag, pp. 366–377.

    Google Scholar 

  • Wood, R.K., (1993), “Deterministic Network Interdiction,” Mathematical and Computer Modeling, Vol. 17, pp. 1–18.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Operations Research Dept., Naual Postgraduate School, Monterey, CA, 93943

    Ahmet Balcioglu & R. Kevin Wood

Authors
  1. Ahmet Balcioglu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Kevin Wood
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of California, Davis

    David L. Woodruff

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Kluwer Academic Publishers

About this chapter

Cite this chapter

Balcioglu, A., Kevin Wood, R. (2003). Enumerating Near-Min S-T Cuts. In: Woodruff, D.L. (eds) Network Interdiction and Stochastic Integer Programming. Operations Research/Computer Science Interfaces Series, vol 22. Springer, Boston, MA. https://doi.org/10.1007/0-306-48109-X_2

Download citation

  • DOI: https://doi.org/10.1007/0-306-48109-X_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4020-7302-1

  • Online ISBN: 978-0-306-48109-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation