This paper presents a combinatorial polynomial-time algorithm for minimizing submodular functions, answering an open question posed in 1981 by GrÃ¶tschel, LovÃ¡sz, and Schrijver. The algorithm employsâ€¦ (More)

Submodular functions are a key concept in combinatorial optimization. One can efficiently solve many optimization problems involving a submodular function, such as computing its minimum value, orâ€¦ (More)

2009 50th Annual IEEE Symposium on Foundations ofâ€¦

2009

This paper addresses the problems of minimizing nonnegative submodular functions under covering constraints, which generalize the vertex cover, edge cover, and set cover problems. We giveâ€¦ (More)

This paper presents a new simple algorithm for minimizing submodular functions. For integer valued submodular functions, the algorithm runs in O(nEO log nM) time, where n is the cardinality of theâ€¦ (More)

Recently, the first combinatorial strongly polynomial algorithms for submodular function minimization have been devised independently by Iwata, Fleischer, and Fujishige and by Schrijver. In thisâ€¦ (More)

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

We consider the wireless relay network model as introduced by Avestimehr, Diggavi and Tse [2] for approximating Gaussian relay channels and show that it is a special case of a more abstract flowâ€¦ (More)

A number of objective functions in clustering problems can b e described with submodular functions. In this paper, we introduce the minim um average cost criterion, and show that the theory ofâ€¦ (More)

The scaling technique was introduced by This paper presents a scaling scheme for submodular functions. A small but strictly submodular function is added before scaling so that the resulting functionsâ€¦ (More)