In this work we show, that for each permuted submodular MinSum problem (Energy Minimization Task) the corresponding submodular MinSum problem can be found in polynomial time. It follows, that permuted submodular MinSum problems are exactly solvable by transforming them into corresponding submodular tasks followed by applying standart approaches (e.g. using MinCutMaxFlow based techniques).

SUMMARY We first describe fundamental results about submodular functions and submodular flows, which lay a basis for devising efficient algorithms for submodular flows. We then give a comprehensive survey on algorithms for submodular flows and show some possible future research directions.

We consider the monotone submodular k-set packing problem in the context of the more general problem of maximizing a monotone submodular function in a k-exchange system. These systems, introduced by Feldman et al. [9], generalize the matroid k-parity problem in a wide class of matroids and capture many other combinatorial optimization problems. We give a deterministic, non-oblivious local searc...

In this paper we develop a framework of submodular optimization algorithms in line with the mirror-descent style of algorithms for convex optimization. We use the fact that a submodular function has both a subdifferential and a superdifferential, which enables us to formulate algorithms for both submodular minimization and maximization. This reveals a unifying framework for a number of submodul...

Many combinatorial problems arising in machine learning can be reduced to the problem of minimizing a submodular function. Submodular functions are a natural discrete analog of convex functions, and can be minimized in strongly polynomial time. Unfortunately, state-of-the-art algorithms for general submodular minimization are intractable for larger problems. In this paper, we introduce a novel ...

In this article we discuss the connection of Rough Set methods and submodular functions. We show that discernibility measure used in reduct calculation is submodular and provides a bridge between certain methods from Rough Set theory and Submodular Function theory.

Author(s): Elbracht, Christian; Kneip, Jakob | Abstract: We show that every structurally submodular separation system admits a canonical tree set which distinguishes its tangles.Mathematics Subject Classifications: 05C40, 05C83, 06A07

A submodular polyhedron is a polyhedron associated with a submodular function. This paper presents a strongly polynomial time algorithm for line search in submodular polyhedra with the aid of a fully combinatorial algorithm for submodular function minimization as a subroutine. The algorithm is based on the parametric search method proposed by Megiddo.

In this paper, we investigate two problems, namely (a) minimizing a submodular cost function under combinatorial constraints, which include cuts, matchings, paths, etc., and (b) optimizing a submodular function under submodular cover and submodular knapsack constraints. While both problems have hardness factors of Ω( √ n) for general submodular cost functions, we show how we can achieve constan...

Submodular functions play a key role in combinatorial optimization and in the study of valued constraint satisfaction problems. Recently, there has been interest in the class of bisubmodular functions, which assign values to disjoint pairs of sets. Like submodular functions, bisubmodular functions can be minimized exactly in polynomial time and exhibit the property of diminishing returns common...