A combinatorial strongly polynomial algorithm for minimizing submodular functions

Satoru Iwata, Lisa Fleischer, Satoru Fujishige
2001 Journal of the ACM  
This paper presents a combinatorial polynomial-time algorithm for minimizing submodular functions, answering an open question posed in 1981 by Grötschel, Lovász, and Schrijver. The algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to the scaled parameter. The resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the length of the largest absolute function value. The paper
more » ... on value. The paper also presents a strongly polynomial version in which the number of steps is bounded by a polynomial in the size of the underlying set, independent of the function values.
doi:10.1145/502090.502096 fatcat:omcg327kcjgspl5ge6xzaujpje