Algorithms for maximum network flow

This paper is a survey, from the point of view of a theoretical computer scientist, of efficient algorithms for the maximum flow problem. Included is a discussion of the most efficient known algorithm for sparse graphs, which makes use of a novel data structure for representing rooted trees. Also discussed are the potential practical significance of the algorithms and open problems.

[1]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[2]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[3]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[4]  Amnon Naamad,et al.  An O(EVlog²V) Algorithm for the Maximal Flow Problem , 1980, J. Comput. Syst. Sci..

[5]  Robert E. Tarjan,et al.  Data structures and network algorithms , 1983, CBMS-NSF regional conference series in applied mathematics.

[6]  Robert E. Tarjan,et al.  A data structure for dynamic trees , 1981, STOC '81.

[7]  Robert B. Dial,et al.  Algorithm 360: shortest-path forest with topological ordering [H] , 1969, CACM.

[8]  Harold N. Gabow,et al.  Scaling algorithms for network problems , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[9]  D. R. Fulkerson,et al.  Flows in Networks. , 1964 .

[10]  S. N. Maheshwari,et al.  An O(|V|³) Algorithm for Finding Maximum Flows in Networks , 1978, Inf. Process. Lett..

[11]  Darwin Klingman,et al.  Comprehensive Computer Evaluation and Enhancement of Maximum Flow Algorithms. , 1979 .

[12]  Uzi Vishkin,et al.  An O(n² log n) Parallel MAX-FLOW Algorithm , 1982, J. Algorithms.

[13]  To-Yat Cheung,et al.  Computational Comparison of Eight Methods for the Maximum Network Flow Problem , 1980, TOMS.

[14]  Richard M. Karp,et al.  Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems , 1972, Combinatorial Optimization.

[15]  R. Tarjan.  A simple version of Karzanov's blocking flow algorithm , 1984 .

[16]  Robert E. Tarjan,et al.  Self-adjusting binary search trees , 1985, JACM.

[17]  D. Sleator.  An 0 (nm log n) algorithm for maximum network flow , 1980 .

[18]  Maurice Queyranne,et al.  Theoretical Efficiency of the Algorithm "Capacity" for the Maximum Flow Problem , 1980, Math. Oper. Res..