论文信息 - A Cost-scaling Algorithm for 0-1 Submodular Flows

A Cost-scaling Algorithm for 0-1 Submodular Flows

Abstract This paper presents a cost-scaling algorithm for minimum cost 0–1 submodular flows. The algorithm works by splitting the arc costs approximately and maintaining an optimal submodular pseudoflow with respect to the split costs obtained by a greedy algorithm. Each scaling phase of the algorithm is a hybrid version of an auction-like method with cost-splitting and a successive-shortest-path method, as a generalization of Orlin and Ahuja's algorithm for the assignment problem.

Satoru Iwata | Maiko Shigeno

[1] Satoru Fujishige,et al. A note on the Frank—Tardos bi-truncation algorithm for crossing-submodular functions , 1992, Math. Program..

[2] J. Edmonds,et al. A Min-Max Relation for Submodular Functions on Graphs , 1977 .

[3] U. ZIMMERMANN,et al. Minimization on submodular flows , 1982, Discret. Appl. Math..

[4] S. Fujishige,et al. AN EFFICIENT COST SCALING ALGORITHM FOR THE INDEPENDENT ASSIGNMENT PROBLEM , 1995 .

[5] Ravindra K. Ahuja,et al. New scaling algorithms for the assignment and minimum mean cycle problems , 1992, Math. Program..

[6] Robert E. Tarjan,et al. Faster Scaling Algorithms for Network Problems , 1989, SIAM J. Comput..

[7] András Frank,et al. Generalized polymatroids and submodular flows , 1988, Math. Program..

[8] Harold N. Gabow. A framework for cost-scaling algorithms for submodular flow problems , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[9] A. Frank,et al. MATROIDS FROM CROSSING FAMILIES , 1984 .

[10] András Frank,et al. Finding feasible vectors of Edmonds-Giles polyhedra , 1984, J. Comb. Theory, Ser. B.

[11] A. Frank. An Algorithm for Submodular Functions on Graphs , 1982 .

[12] Satoru Fujishige,et al. Submodular functions and optimization , 1991 .

[13] Ying Xu,et al. Efficient algorithms for independent assignment on graphic and linear matroids , 1989, 30th Annual Symposium on Foundations of Computer Science.