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Network Flows

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

Keywords

Undirected Graph Network Flow Parallel Edge Minimum Capacity Distance Label 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

General Literature

  1. Ahuja, R.K., Magnanti, T.L., and Orlin, J.B. [1993]: Network Flows. Prentice-Hall, Englewood Cliffs 1993Google Scholar
  2. Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., and Schrijver, A. [1998]: Combinatorial Optimization. Wiley, New York 1998, Chapter 3MATHGoogle Scholar
  3. Cormen, T.H., Leiserson, C.E., and Rivest, R.L. [1990]: Introduction to Algorithms. MITPress, Cambridge 1990, Chapter 27Google Scholar
  4. Ford, L.R., and Fulkerson, D.R. [1962]: Flows in Networks. Princeton University Press, Princeton 1962MATHGoogle Scholar
  5. Frank, A. [1995]: Connectivity and network flows. In: Handbook of Combinatorics; Vol. 1 (R.L. Graham, M. Grötschel, L. Lovász, eds.), Elsevier, Amsterdam, 1995Google Scholar
  6. 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. 101–164Google Scholar
  7. Gondran, M., and Minoux, M. [1984]: Graphs and Algorithms. Wiley, Chichester 1984, Chapter 5MATHGoogle Scholar
  8. Jungnickel, D. [1999]: Graphs, Networks and Algorithms. Springer, Berlin 1999Google Scholar
  9. Phillips, D.T., and Garcia-Diaz, A. [1981]: Fundamentals of Network Analysis. Prentice-Hall, Englewood Cliffs 1981MATHGoogle Scholar
  10. Ruhe, G. [1991]: Algorithmic Aspects of Flows in Networks. Kluwer Academic Publishers, Dordrecht 1991MATHGoogle Scholar
  11. Schrijver, A. [2003]: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Berlin 2003, Chapters 9,10,13–15MATHGoogle Scholar
  12. Tarjan, R.E. [1983]: Data Structures and Network Algorithms. SIAM, Philadelphia 1983, Chapter 8Google Scholar
  13. Thulasiraman, K., and Swamy, M.N.S. [1992]: Graphs: Theory and Algorithms. Wiley, New York 1992, Chapter 12MATHGoogle Scholar

Cited References

  1. 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), 939–954CrossRefMathSciNetMATHGoogle Scholar
  2. Cheriyan, J., and Maheshwari, S.N. [1989]: Analysis of preflow push algorithms for maximum network flow. SIAM Journal on Computing 18 (1989), 1057–1086CrossRefMathSciNetMATHGoogle Scholar
  3. 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), 239–242CrossRefMathSciNetGoogle Scholar
  4. 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
  5. 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. 114–125Google Scholar
  6. 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), 864–894CrossRefMathSciNetMATHGoogle Scholar
  7. 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. 215–221Google Scholar
  8. Dinic, E.A. [1970]: Algorithm for solution of a problem of maximum flow in a network with power estimation. Soviet Mathematics Doklady 11 (1970), 1277–1280MATHGoogle Scholar
  9. Edmonds, J., and Karp, R.M. [1972]: Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM 19 (1972), 248–264CrossRefMATHGoogle Scholar
  10. Elias, P., Feinstein, A., and Shannon, C.E. [1956]: Note on maximum flow through a network. IRE Transactions on Information Theory, IT-2 (1956), 117–119Google Scholar
  11. Ford, L.R., and Fulkerson, D.R. [1956]: Maximal Flow Through a Network. Canadian Journal of Mathematics 8 (1956), 399–404MathSciNetMATHGoogle Scholar
  12. 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), 210–218MathSciNetMATHGoogle Scholar
  13. Frank, A. [1994]: On the edge-connectivity algorithm of Nagamochi and Ibaraki. Laboratoire Artemis, IMAG, Université J. Fourier, Grenoble, 1994Google Scholar
  14. Fujishige, S. [2003]: A maximum flow algorithm using MA ordering. Operations Research Letters 31 (2003), 176–178CrossRefMathSciNetMATHGoogle Scholar
  15. Gabow, H.N. [1995]: A matroid approach to finding edge connectivity and packing arborescences. Journal of Computer and System Sciences 50 (1995), 259–273CrossRefMathSciNetMATHGoogle Scholar
  16. Galil, Z. [1980]: An O(V 5/3 E 2/3) algorithm for the maximal flow problem. Acta Informatica 14 (1980), 221–242MathSciNetMATHGoogle Scholar
  17. 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), 203–217CrossRefMathSciNetMATHGoogle Scholar
  18. Gallai, T. [1958]: Maximum-minimum Sätze über Graphen. Acta Mathematica Academiae Scientiarum Hungaricae 9 (1958), 395–434CrossRefMathSciNetMATHGoogle Scholar
  19. Goldberg, A.V., and Rao, S. [1998]: Beyond the flow decomposition barrier. Journal of the ACM 45 (1998), 783–797CrossRefMathSciNetMATHGoogle Scholar
  20. Goldberg, A.V., and Tarjan, R.E. [1988]: A new approach to the maximum flow problem. Journal of the ACM 35 (1988), 921–940CrossRefMathSciNetMATHGoogle Scholar
  21. Gomory, R.E., and Hu, T.C. [1961]: Multi-terminal network flows. Journal of SIAM 9 (1961), 551–570MathSciNetMATHGoogle Scholar
  22. Gusfield, D. [1990]: Very simple methods for all pairs network flow analysis. SIAM Journal on Computing 19 (1990), 143–155CrossRefMathSciNetMATHGoogle Scholar
  23. Hao, J., and Orlin, J.B. [1994]: A faster algorithm for finding the minimum cut in a directed graph. Journal of Algorithms 17 (1994), 409–423CrossRefMathSciNetGoogle Scholar
  24. Henzinger, M.R., Rao, S., and Gabow, H.N. [2000]: Computing vertex connectivity: new bounds from old techniques. Journal of Algorithms 34 (2000), 222–250CrossRefMathSciNetMATHGoogle Scholar
  25. 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. 113–128Google Scholar
  26. Hu, T.C. [1969]: Integer Programming and Network Flows. Addison-Wesley, Reading 1969MATHGoogle Scholar
  27. Karger, D.R. [2000]: Minimum cuts in near-linear time. Journal of the ACM 47 (2000), 46–76CrossRefMathSciNetMATHGoogle Scholar
  28. 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), 69–78Google Scholar
  29. Karger, D.R., and Stein, C. [1996]: A new approach to the minimum cut problem. Journal of the ACM 43 (1996), 601–640CrossRefMathSciNetMATHGoogle Scholar
  30. Karzanov, A.V. [1974]: Determining the maximal flow in a network by the method of preflows. Soviet Mathematics Doklady 15 (1974), 434–437MATHGoogle Scholar
  31. King, V., Rao, S., and Tarjan, R.E. [1994]: A faster deterministic maximum flow algorithm. Journal of Algorithms 17 (1994), 447–474CrossRefMathSciNetGoogle Scholar
  32. Mader, W. [1972]: Über minimal n-fach zusammenhängende, unendliche Graphen und ein Extremalproblem. Arch. Math. 23 (1972), 553–560MathSciNetMATHGoogle Scholar
  33. Mader, W. [1981]: On a property of n edge-connected digraphs. Combinatorica 1 (1981), 385–386MathSciNetMATHGoogle Scholar
  34. 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), 277–278CrossRefMathSciNetMATHGoogle Scholar
  35. Menger, K. [1927]: Zur allgemeinen Kurventheorie. Fundamenta Mathematicae 10 (1927), 96–115MATHGoogle Scholar
  36. Nagamochi, H., and Ibaraki, T. [1992]: Computing edge-connectivity in multigraphs and capacitated graphs. SIAM Journal on Discrete Mathematics 5 (1992), 54–66CrossRefMathSciNetMATHGoogle Scholar
  37. Nagamochi, H., and Ibaraki, T. [2000]: A fast algorithm for computing minimum 3-way and 4-way cuts. Mathematical Programming 88 (2000), 507–520MathSciNetMATHGoogle Scholar
  38. Phillips, S., and Dessouky, M.I. [1977]: Solving the project time/cost tradeoff problem using the minimal cut concept. Management Science 24 (1977), 393–400CrossRefMATHGoogle Scholar
  39. Picard, J., and Queyranne, M. [1980]: On the structure of all minimum cuts in a network and applications. Mathematical Programming Study 13 (1980), 8–16MathSciNetMATHGoogle Scholar
  40. Queyranne, M. [1998]: Minimizing symmetric submodular functions. Mathematical Programming B 82 (1998), 3–12MathSciNetMATHGoogle Scholar
  41. Rose, D.J. [1970]: Triangulated graphs and the elimination process. Journal of Mathematical Analysis and Applications 32 (1970), 597–609CrossRefMathSciNetMATHGoogle Scholar
  42. Shiloach, Y. [1978]: An O(nI log2 I ) maximum-flow algorithm. Technical Report STANCS-78-802, Computer Science Department, Stanford University, 1978Google Scholar
  43. Shiloach, Y. [1979]: Edge-disjoint branching in directed multigraphs. Information Processing Letters 8 (1979), 24–27MathSciNetMATHGoogle Scholar
  44. Shioura, A. [2004]: The MA ordering max-flow algorithm is not strongly polynomial for directed networks. Operations Research Letters 32 (2004), 31–35CrossRefMathSciNetMATHGoogle Scholar
  45. 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, 1978Google Scholar
  46. Sleator, D.D., and Tarjan, R.E. [1983]: A data structure for dynamic trees. Journal of Computer and System Sciences 26 (1983), 362–391CrossRefMathSciNetMATHGoogle Scholar
  47. Su, X.Y. [1997]: Some generalizations of Menger’s theorem concerning arc-connected digraphs. Discrete Mathematics 175 (1997), 293–296CrossRefMathSciNetMATHGoogle Scholar
  48. Stoer, M., and Wagner, F. [1997]: A simple min cut algorithm. Journal of the ACM 44 (1997), 585–591CrossRefMathSciNetMATHGoogle Scholar
  49. Tunçel, L. [1994]: On the complexity preflow-push algorithms for maximum flow problems. Algorithmica 11 (1994), 353–359MathSciNetMATHGoogle Scholar
  50. 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. 366–377Google Scholar
  51. Vygen, J. [2002]: On dual minimum cost flow algorithms. Mathematical Methods of Operations Research 56 (2002), 101–126MathSciNetMATHGoogle Scholar
  52. Weihe, K. [1997]: V log V ) time. Journal of Computer and System Sciences 55 (1997), 454–475CrossRefMathSciNetMATHGoogle Scholar
  53. Whitney, H. [1932]: Congruent graphs and the connectivity of graphs. American Journal of Mathematics 54 (1932), 150–168MathSciNetMATHGoogle Scholar

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