Skip to main content

Part of the book series: Algorithms and Combinatorics 21 ((AC,volume 21))

  • 3839 Accesses

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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

General Literature

  • Ahuja, R.K., Magnanti, T.L., and Orlin, J.B. [1993]: Network Flows. Prentice-Hall, Englewood Cliffs 1993

    Google Scholar 

  • Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., and Schrijver, A. [1998]: Combinatorial Optimization. Wiley, New York 1998, Chapter 3

    MATH  Google Scholar 

  • Cormen, T.H., Leiserson, C.E., and Rivest, R.L. [1990]: Introduction to Algorithms. MITPress, Cambridge 1990, Chapter 27

    Google Scholar 

  • Ford, L.R., and Fulkerson, D.R. [1962]: Flows in Networks. Princeton University Press, Princeton 1962

    MATH  Google Scholar 

  • Frank, A. [1995]: Connectivity and network flows. In: Handbook of Combinatorics; Vol. 1 (R.L. Graham, M. Grötschel, L. Lovász, eds.), Elsevier, Amsterdam, 1995

    Google Scholar 

  • Goldberg, A.V., Tardos, É., and Tarjan, R.E. [1990]: Network flow algorithms. In: Paths, Flows, and VLSI-Layout (B. Korte, L. Lovász, H.J. Prömel, A. Schrijver, eds.), Springer, Berlin 1990, pp. 101–164

    Google Scholar 

  • Gondran, M., and Minoux, M. [1984]: Graphs and Algorithms. Wiley, Chichester 1984, Chapter 5

    MATH  Google Scholar 

  • Jungnickel, D. [1999]: Graphs, Networks and Algorithms. Springer, Berlin 1999

    Google Scholar 

  • Phillips, D.T., and Garcia-Diaz, A. [1981]: Fundamentals of Network Analysis. Prentice-Hall, Englewood Cliffs 1981

    MATH  Google Scholar 

  • Ruhe, G. [1991]: Algorithmic Aspects of Flows in Networks. Kluwer Academic Publishers, Dordrecht 1991

    MATH  Google Scholar 

  • Schrijver, A. [2003]: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Berlin 2003, Chapters 9,10,13–15

    MATH  Google Scholar 

  • Tarjan, R.E. [1983]: Data Structures and Network Algorithms. SIAM, Philadelphia 1983, Chapter 8

    Google Scholar 

  • Thulasiraman, K., and Swamy, M.N.S. [1992]: Graphs: Theory and Algorithms. Wiley, New York 1992, Chapter 12

    MATH  Google Scholar 

Cited References

  • Ahuja, R.K., Orlin, J.B., and Tarjan, R.E. [1989]: Improved time bounds for the maximum flow problem. SIAM Journal on Computing 18 (1989), 939–954

    Article  MathSciNet  MATH  Google Scholar 

  • Cheriyan, J., and Maheshwari, S.N. [1989]: Analysis of preflow push algorithms for maximum network flow. SIAM Journal on Computing 18 (1989), 1057–1086

    Article  MathSciNet  MATH  Google Scholar 

  • Cheriyan, J., and Mehlhorn, K. [1999]: An analysis of the highest-level selection rule in the preflow-push max-flow algorithm. Information Processing Letters 69 (1999), 239–242

    Article  MathSciNet  Google Scholar 

  • Cherkassky, B.V. [1977]: Algorithm of construction of maximal flow in networks with complexity of O(V2√E) operations. Mathematical Methods of Solution of Economical Problems 7 (1977), 112–125 [in Russian]

    Google Scholar 

  • Cunningham, W.H., and Tang, L. [1999]: Optimal 3-terminal cuts and linear programming. Proceedings of the 7th Conference on Integer Programming and Combinatorial Optimization; LNCS 1610 (G. Cornuéjols, R.E. Burkard, G.J. Woeginger, eds.), Springer, Berlin 1999, pp. 114–125

    Google Scholar 

  • Dahlhaus, E., Johnson, D.S., Papadimitriou, C.H., Seymour, P.D., and Yannakakis, M. [1994]: The complexity of multiterminal cuts. SIAM Journal on Computing 23 (1994), 864–894

    Article  MathSciNet  MATH  Google Scholar 

  • Dantzig, G.B., and Fulkerson, D.R. [1956]: On the max-flow min-cut theorem of networks. In: Linear Inequalities and Related Systems (H.W. Kuhn, A.W. Tucker, eds.), Princeton University Press, Princeton 1956, pp. 215–221

    Google Scholar 

  • Dinic, E.A. [1970]: Algorithm for solution of a problem of maximum flow in a network with power estimation. Soviet Mathematics Doklady 11 (1970), 1277–1280

    MATH  Google Scholar 

  • Edmonds, J., and Karp, R.M. [1972]: Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM 19 (1972), 248–264

    Article  MATH  Google Scholar 

  • Elias, P., Feinstein, A., and Shannon, C.E. [1956]: Note on maximum flow through a network. IRE Transactions on Information Theory, IT-2 (1956), 117–119

    Google Scholar 

  • Ford, L.R., and Fulkerson, D.R. [1956]: Maximal Flow Through a Network. Canadian Journal of Mathematics 8 (1956), 399–404

    MathSciNet  MATH  Google Scholar 

  • Ford, L.R., and Fulkerson, D.R. [1957]: A simple algorithm for finding maximal network flows and an application to the Hitchcock problem. Canadian Journal of Mathematics 9 (1957), 210–218

    MathSciNet  MATH  Google Scholar 

  • Frank, A. [1994]: On the edge-connectivity algorithm of Nagamochi and Ibaraki. Laboratoire Artemis, IMAG, Université J. Fourier, Grenoble, 1994

    Google Scholar 

  • Fujishige, S. [2003]: A maximum flow algorithm using MA ordering. Operations Research Letters 31 (2003), 176–178

    Article  MathSciNet  MATH  Google Scholar 

  • Gabow, H.N. [1995]: A matroid approach to finding edge connectivity and packing arborescences. Journal of Computer and System Sciences 50 (1995), 259–273

    Article  MathSciNet  MATH  Google Scholar 

  • Galil, Z. [1980]: An O(V 5/3 E 2/3) algorithm for the maximal flow problem. Acta Informatica 14 (1980), 221–242

    MathSciNet  MATH  Google Scholar 

  • Galil, Z., and Namaad, A. [1980]: An O(EV log2 V) algorithm for the maximal flow problem. Journal of Computer and System Sciences 21 (1980), 203–217

    Article  MathSciNet  MATH  Google Scholar 

  • Gallai, T. [1958]: Maximum-minimum Sätze über Graphen. Acta Mathematica Academiae Scientiarum Hungaricae 9 (1958), 395–434

    Article  MathSciNet  MATH  Google Scholar 

  • Goldberg, A.V., and Rao, S. [1998]: Beyond the flow decomposition barrier. Journal of the ACM 45 (1998), 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 35 (1988), 921–940

    Article  MathSciNet  MATH  Google Scholar 

  • Gomory, R.E., and Hu, T.C. [1961]: Multi-terminal network flows. Journal of SIAM 9 (1961), 551–570

    MathSciNet  MATH  Google Scholar 

  • Gusfield, D. [1990]: Very simple methods for all pairs network flow analysis. SIAM Journal on Computing 19 (1990), 143–155

    Article  MathSciNet  MATH  Google Scholar 

  • Hao, J., and Orlin, J.B. [1994]: A faster algorithm for finding the minimum cut in a directed graph. Journal of Algorithms 17 (1994), 409–423

    Article  MathSciNet  Google Scholar 

  • Henzinger, M.R., Rao, S., and Gabow, H.N. [2000]: Computing vertex connectivity: new bounds from old techniques. Journal of Algorithms 34 (2000), 222–250

    Article  MathSciNet  MATH  Google Scholar 

  • Hoffman, A.J. [1960]: Some recent applications of the theory of linear inequalities to extremal combinatorial analysis. In: Combinatorial Analysis (R.E. Bellman, M. Hall, eds.), AMS, Providence 1960, pp. 113–128

    Google Scholar 

  • Hu, T.C. [1969]: Integer Programming and Network Flows. Addison-Wesley, Reading 1969

    MATH  Google Scholar 

  • Karger, D.R. [2000]: Minimum cuts in near-linear time. Journal of the ACM 47 (2000), 46–76

    Article  MathSciNet  MATH  Google Scholar 

  • Karger, D.R., and Levine, M.S. [1998]: Finding maximum flows in undirected graphs seems easier than bipartite matching. Proceedings of the 30th Annual ACM Symposium on the Theory of Computing (1998), 69–78

    Google Scholar 

  • Karger, D.R., and Stein, C. [1996]: A new approach to the minimum cut problem. Journal of the ACM 43 (1996), 601–640

    Article  MathSciNet  MATH  Google Scholar 

  • Karzanov, A.V. [1974]: Determining the maximal flow in a network by the method of preflows. Soviet Mathematics Doklady 15 (1974), 434–437

    MATH  Google Scholar 

  • King, V., Rao, S., and Tarjan, R.E. [1994]: A faster deterministic maximum flow algorithm. Journal of Algorithms 17 (1994), 447–474

    Article  MathSciNet  Google Scholar 

  • Mader, W. [1972]: Über minimal n-fach zusammenhängende, unendliche Graphen und ein Extremalproblem. Arch. Math. 23 (1972), 553–560

    MathSciNet  MATH  Google Scholar 

  • Mader, W. [1981]: On a property of n edge-connected digraphs. Combinatorica 1 (1981), 385–386

    MathSciNet  MATH  Google Scholar 

  • Malhotra, V.M., Kumar, M.P., and Maheshwari, S.N. [1978]: V 3) algorithm for finding maximum flows in networks. Information Processing Letters 7 (1978), 277–278

    Article  MathSciNet  MATH  Google Scholar 

  • Menger, K. [1927]: Zur allgemeinen Kurventheorie. Fundamenta Mathematicae 10 (1927), 96–115

    MATH  Google Scholar 

  • Nagamochi, H., and Ibaraki, T. [1992]: Computing edge-connectivity in multigraphs and capacitated graphs. SIAM Journal on Discrete Mathematics 5 (1992), 54–66

    Article  MathSciNet  MATH  Google Scholar 

  • Nagamochi, H., and Ibaraki, T. [2000]: A fast algorithm for computing minimum 3-way and 4-way cuts. Mathematical Programming 88 (2000), 507–520

    MathSciNet  MATH  Google Scholar 

  • Phillips, S., and Dessouky, M.I. [1977]: Solving the project time/cost tradeoff problem using the minimal cut concept. Management Science 24 (1977), 393–400

    Article  MATH  Google Scholar 

  • Picard, J., and Queyranne, M. [1980]: On the structure of all minimum cuts in a network and applications. Mathematical Programming Study 13 (1980), 8–16

    MathSciNet  MATH  Google Scholar 

  • Queyranne, M. [1998]: Minimizing symmetric submodular functions. Mathematical Programming B 82 (1998), 3–12

    MathSciNet  MATH  Google Scholar 

  • Rose, D.J. [1970]: Triangulated graphs and the elimination process. Journal of Mathematical Analysis and Applications 32 (1970), 597–609

    Article  MathSciNet  MATH  Google Scholar 

  • Shiloach, Y. [1978]: An O(nI log2 I ) maximum-flow algorithm. Technical Report STANCS-78-802, Computer Science Department, Stanford University, 1978

    Google Scholar 

  • Shiloach, Y. [1979]: Edge-disjoint branching in directed multigraphs. Information Processing Letters 8 (1979), 24–27

    MathSciNet  MATH  Google Scholar 

  • Shioura, A. [2004]: The MA ordering max-flow algorithm is not strongly polynomial for directed networks. Operations Research Letters 32 (2004), 31–35

    Article  MathSciNet  MATH  Google Scholar 

  • Sleator, D.D. [1980]: An O(nm log n) algorithm for maximum network flow. Technical Report STAN-CS-80-831, Computer Science Department, Stanford University, 1978

    Google Scholar 

  • Sleator, D.D., and Tarjan, R.E. [1983]: A data structure for dynamic trees. Journal of Computer and System Sciences 26 (1983), 362–391

    Article  MathSciNet  MATH  Google Scholar 

  • Su, X.Y. [1997]: Some generalizations of Menger’s theorem concerning arc-connected digraphs. Discrete Mathematics 175 (1997), 293–296

    Article  MathSciNet  MATH  Google Scholar 

  • Stoer, M., and Wagner, F. [1997]: A simple min cut algorithm. Journal of the ACM 44 (1997), 585–591

    Article  MathSciNet  MATH  Google Scholar 

  • Tunçel, L. [1994]: On the complexity preflow-push algorithms for maximum flow problems. Algorithmica 11 (1994), 353–359

    MathSciNet  MATH  Google Scholar 

  • Vazirani, V.V., and Yannakakis, M. [1992]: Suboptimal cuts: their enumeration, weight, and number. In: Automata, Languages and Programming; Proceedings; LNCS 623 (W. Kuich, ed.), Springer, Berlin 1992, pp. 366–377

    Google Scholar 

  • Vygen, J. [2002]: On dual minimum cost flow algorithms. Mathematical Methods of Operations Research 56 (2002), 101–126

    MathSciNet  MATH  Google Scholar 

  • Weihe, K. [1997]: V log V ) time. Journal of Computer and System Sciences 55 (1997), 454–475

    Article  MathSciNet  MATH  Google Scholar 

  • Whitney, H. [1932]: Congruent graphs and the connectivity of graphs. American Journal of Mathematics 54 (1932), 150–168

    MathSciNet  MATH  Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2006). Network Flows. In: Combinatorial Optimization. Algorithms and Combinatorics 21, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29297-7_8

Download citation

Publish with us

Policies and ethics