论文信息 - An efficient algorithm for the minimum capacity cut problem

An efficient algorithm for the minimum capacity cut problem

Given a finite undirected graph with nonnegative edge capacities the minimum capacity cut problem consists of partitioning the graph into two nonempty sets such that the sum of the capacities of edges connecting the two parts is minimum among all possible partitionings. The standard algorithm to calculate a minimum capacity cut, due to Gomory and Hu (1961), runs in O(n4) time and is difficult to implement. We present an alternative algorithm with the same worst-case bound which is easier to implement and which was found empirically to be far superior to the standard algorithm. We report computational results for graphs with up to 2000 nodes.

Giovanni Rinaldi | Manfred W. Padberg | M. Padberg | G. Rinaldi

[1] Laurence A. Wolsey,et al. Trees and Cuts , 1983 .

[2] Giovanni Rinaldi,et al. A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems , 1991, SIAM Rev..

[3] Peter Elias,et al. A note on the maximum flow through a network , 1956, IRE Trans. Inf. Theory.

[4] H. Crowder,et al. Solving Large-Scale Symmetric Travelling Salesman Problems to Optimality , 1980 .

[5] T. C. Hu,et al. Multi-Terminal Network Flows , 1961 .

[6] M. Padberg,et al. Addendum: Optimization of a 532-city symmetric traveling salesman problem by branch and cut , 1990 .

[7] J. P. Secrétan,et al. Der Saccus endolymphaticus bei Entzündungsprozessen , 1944 .

[8] J. Picard,et al. Selected Applications of Minimum Cuts in Networks , 1982 .

[9] D. R. Fulkerson,et al. Maximal Flow Through a Network , 1956 .

[10] Ted G. Lewis,et al. Generalized Feedback Shift Register Pseudorandom Number Algorithm , 1973, JACM.

[11] Andrew V. Goldberg,et al. A new approach to the maximum flow problem , 1986, STOC '86.

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