Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
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
Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., and Schrijver, A. [1998]: Combinatorial Optimization. Wiley, New York 1998, Chapter 3
Cormen, T.H., Leiserson, C.E., and Rivest, R.L. [1990]: Introduction to Algorithms. MITPress, Cambridge 1990, Chapter 27
Ford, L.R., and Fulkerson, D.R. [1962]: Flows in Networks. Princeton University Press, Princeton 1962
Frank, A. [1995]: Connectivity and network flows. In: Handbook of Combinatorics; Vol. 1 (R.L. Graham, M. Grötschel, L. Lovász, eds.), Elsevier, Amsterdam, 1995
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
Gondran, M., and Minoux, M. [1984]: Graphs and Algorithms. Wiley, Chichester 1984, Chapter 5
Jungnickel, D. [1999]: Graphs, Networks and Algorithms. Springer, Berlin 1999
Phillips, D.T., and Garcia-Diaz, A. [1981]: Fundamentals of Network Analysis. Prentice-Hall, Englewood Cliffs 1981
Ruhe, G. [1991]: Algorithmic Aspects of Flows in Networks. Kluwer Academic Publishers, Dordrecht 1991
Schrijver, A. [2003]: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Berlin 2003, Chapters 9,10,13–15
Tarjan, R.E. [1983]: Data Structures and Network Algorithms. SIAM, Philadelphia 1983, Chapter 8
Thulasiraman, K., and Swamy, M.N.S. [1992]: Graphs: Theory and Algorithms. Wiley, New York 1992, Chapter 12
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
Cheriyan, J., and Maheshwari, S.N. [1989]: Analysis of preflow push algorithms for maximum network flow. SIAM Journal on Computing 18 (1989), 1057–1086
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
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]
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
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
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
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
Edmonds, J., and Karp, R.M. [1972]: Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM 19 (1972), 248–264
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
Ford, L.R., and Fulkerson, D.R. [1956]: Maximal Flow Through a Network. Canadian Journal of Mathematics 8 (1956), 399–404
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
Frank, A. [1994]: On the edge-connectivity algorithm of Nagamochi and Ibaraki. Laboratoire Artemis, IMAG, Université J. Fourier, Grenoble, 1994
Fujishige, S. [2003]: A maximum flow algorithm using MA ordering. Operations Research Letters 31 (2003), 176–178
Gabow, H.N. [1995]: A matroid approach to finding edge connectivity and packing arborescences. Journal of Computer and System Sciences 50 (1995), 259–273
Galil, Z. [1980]: An O(V 5/3 E 2/3) algorithm for the maximal flow problem. Acta Informatica 14 (1980), 221–242
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
Gallai, T. [1958]: Maximum-minimum Sätze über Graphen. Acta Mathematica Academiae Scientiarum Hungaricae 9 (1958), 395–434
Goldberg, A.V., and Rao, S. [1998]: Beyond the flow decomposition barrier. Journal of the ACM 45 (1998), 783–797
Goldberg, A.V., and Tarjan, R.E. [1988]: A new approach to the maximum flow problem. Journal of the ACM 35 (1988), 921–940
Gomory, R.E., and Hu, T.C. [1961]: Multi-terminal network flows. Journal of SIAM 9 (1961), 551–570
Gusfield, D. [1990]: Very simple methods for all pairs network flow analysis. SIAM Journal on Computing 19 (1990), 143–155
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
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
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
Hu, T.C. [1969]: Integer Programming and Network Flows. Addison-Wesley, Reading 1969
Karger, D.R. [2000]: Minimum cuts in near-linear time. Journal of the ACM 47 (2000), 46–76
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
Karger, D.R., and Stein, C. [1996]: A new approach to the minimum cut problem. Journal of the ACM 43 (1996), 601–640
Karzanov, A.V. [1974]: Determining the maximal flow in a network by the method of preflows. Soviet Mathematics Doklady 15 (1974), 434–437
King, V., Rao, S., and Tarjan, R.E. [1994]: A faster deterministic maximum flow algorithm. Journal of Algorithms 17 (1994), 447–474
Mader, W. [1972]: Über minimal n-fach zusammenhängende, unendliche Graphen und ein Extremalproblem. Arch. Math. 23 (1972), 553–560
Mader, W. [1981]: On a property of n edge-connected digraphs. Combinatorica 1 (1981), 385–386
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
Menger, K. [1927]: Zur allgemeinen Kurventheorie. Fundamenta Mathematicae 10 (1927), 96–115
Nagamochi, H., and Ibaraki, T. [1992]: Computing edge-connectivity in multigraphs and capacitated graphs. SIAM Journal on Discrete Mathematics 5 (1992), 54–66
Nagamochi, H., and Ibaraki, T. [2000]: A fast algorithm for computing minimum 3-way and 4-way cuts. Mathematical Programming 88 (2000), 507–520
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
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
Queyranne, M. [1998]: Minimizing symmetric submodular functions. Mathematical Programming B 82 (1998), 3–12
Rose, D.J. [1970]: Triangulated graphs and the elimination process. Journal of Mathematical Analysis and Applications 32 (1970), 597–609
Shiloach, Y. [1978]: An O(nI log2 I ) maximum-flow algorithm. Technical Report STANCS-78-802, Computer Science Department, Stanford University, 1978
Shiloach, Y. [1979]: Edge-disjoint branching in directed multigraphs. Information Processing Letters 8 (1979), 24–27
Shioura, A. [2004]: The MA ordering max-flow algorithm is not strongly polynomial for directed networks. Operations Research Letters 32 (2004), 31–35
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
Sleator, D.D., and Tarjan, R.E. [1983]: A data structure for dynamic trees. Journal of Computer and System Sciences 26 (1983), 362–391
Su, X.Y. [1997]: Some generalizations of Menger’s theorem concerning arc-connected digraphs. Discrete Mathematics 175 (1997), 293–296
Stoer, M., and Wagner, F. [1997]: A simple min cut algorithm. Journal of the ACM 44 (1997), 585–591
Tunçel, L. [1994]: On the complexity preflow-push algorithms for maximum flow problems. Algorithmica 11 (1994), 353–359
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
Vygen, J. [2002]: On dual minimum cost flow algorithms. Mathematical Methods of Operations Research 56 (2002), 101–126
Weihe, K. [1997]: V log V ) time. Journal of Computer and System Sciences 55 (1997), 454–475
Whitney, H. [1932]: Congruent graphs and the connectivity of graphs. American Journal of Mathematics 54 (1932), 150–168
Rights 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
DOI: https://doi.org/10.1007/3-540-29297-7_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25684-7
Online ISBN: 978-3-540-29297-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)