A fully combinatorial algorithm for submodular function minimization

This paper presents a strongly polynomial algorithm for submodular function minimization using only additions, subtractions, comparisons, and oracle calls for function values.

[1]  L. Shapley Cores of convex games , 1971 .

[2]  Satoru Fujishige,et al.  Lexicographically Optimal Base of a Polymatroid with Respect to a Weight Vector , 1980, Math. Oper. Res..

[3]  Martin Grötschel,et al.  The ellipsoid method and its consequences in combinatorial optimization , 1981, Comb..

[4]  L. Lovász,et al.  Geometric Algorithms and Combinatorial Optimization , 1981 .

[5]  László Lovász,et al.  Submodular functions and convexity , 1982, ISMP.

[6]  S. Fujishige,et al.  A NOTE ON SUBMODULAR FUNCTIONS ON DISTRIBUTIVE LATTICES , 1983 .

[7]  S. Fujishige Submodular systems and related topics , 1984 .

[8]  William H. Cunningham,et al.  Testing membership in matroid polyhedra , 1984, J. Comb. Theory, Ser. B.

[9]  Éva Tardos,et al.  A strongly polynomial minimum cost circulation algorithm , 1985, Comb..

[10]  William H. Cunningham On submodular function minimization , 1985, Comb..

[11]  Satoru Fujishige,et al.  A capacity-rounding algorithm for the minimum-cost circulation problem: A dual framework of the Tardos algorithm , 1986, Math. Program..

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

[13]  藤重 悟 Submodular functions and optimization , 1991 .

[14]  Toshihide Ibaraki,et al.  Computing Edge-Connectivity in Multigraphs and Capacitated Graphs , 1992, SIAM J. Discret. Math..

[15]  Michel X. Goemans,et al.  Minimizing submodular functions over families of sets , 1995, Comb..

[16]  Satoru Iwata,et al.  A capacity scaling algorithm for convex cost submodular flows , 1996, SODA '96.

[17]  Maurice Queyranne,et al.  Minimizing symmetric submodular functions , 1998, Math. Program..

[18]  Alexander Schrijver,et al.  A Combinatorial Algorithm Minimizing Submodular Functions in Strongly Polynomial Time , 2000, J. Comb. Theory B.

[19]  Satoru Iwata,et al.  A combinatorial strongly polynomial algorithm for minimizing submodular functions , 2001, JACM.

[20]  Jack Edmonds,et al.  Submodular Functions, Matroids, and Certain Polyhedra , 2001, Combinatorial Optimization.

[21]  Satoru Iwata,et al.  A faster capacity scaling algorithm for minimum cost submodular flow , 2002, Math. Program..

[22]  Satoru Iwata A Faster Scaling Algorithm for Minimizing Submodular Functions , 2003, SIAM J. Comput..

[23]  Satoru Iwata,et al.  A push-relabel framework for submodular function minimization and applications to parametric optimization , 2003, Discret. Appl. Math..