A push-relabel framework for submodular function minimization and applications to parametric optimization

A Push-Relabel Framework for Submodular Function Minimization and Applications to Parametric Optimization

Simple Push-relabel Algorithms for Matroids and Submodular Flows

We derive simple push-relabel algorithms for the matroid partitioning, matroid membership, and submodular flow feasibility problems. It turns out that, in order to have a strongly polynomial algorithm, the lexicographic rule used in all previous algorithms for the two latter problems can be avoided. Its proper role is that it helps speeding up the algorithm in the last problem.

A fast cost scaling algorithm for submodular flow

This paper presents the current fastest known weakly polynomial algorithm for the submodular flow problem when the costs are not too big. It combines Röck’s or Bland and Jensen’s cost scaling algorithms, Cunningham and Frank’s primal-dual algorithm for submodular flow, and Fujishige and Zhang’s push-relabel algorithm for submodular maximum flow to get a running time of O(nh logC), where n is th...

A strongly polynomial algorithm for line search in submodular polyhedra

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. The algorithm is based on the parametric search method proposed by Megiddo.

Some Results about the Contractions and the Pendant Pairs of a Submodular System

Submodularity is an important  property of set functions with deep theoretical results  and various  applications. Submodular systems appear in many applicable area, for example machine learning, economics, computer vision, social science, game theory and combinatorial optimization.  Nowadays submodular functions optimization has been attracted by many researchers.  Pendant pairs of a symmetric...