A dual algorithm for submodular flow problems

A dual algorithm for submodular flow problems

The submodular flow (SF) problem, introduced by Edmonds and Giles [6], is a general network flow problem, where net flows into subsets of nodes are restricted by submodular set constraints. Suppose that we are given (i) a directed graph G = (V, E) with node set V and arc set E, (ii) a submodular function b" on a crossing family ,~-", (iii) lower and upper capacity functions f a n d g where f : ...

Capacity scaling algorithm for scalable M-convex submodular flow problems

An M-convex function is a nonlinear discrete function defined on integer points introduced by Murota in 1996, and the M-convex submodular flow problem is one of the most general frameworks of efficiently solvable combinatorial optimization problems. It includes the minimum cost flow and the submodular flow problems as its special cases. In this paper, we first devise a successive shortest path ...

A Framework for Cost-scaling Algorithms for Submodular Flow Problems

A Faster Capacity Scaling Algorithm for Minimum Cost Submodular Flow

A Capacity Scaling Algorithm for M-convex Submodular Flow

This paper presents a faster algorithm for the M-convex submodular flow problem, which is a generalization of the minimum-cost flow problem with an M-convex cost function for the flow-boundary, where an M-convex function is a nonlinear nonseparable discrete convex function on integer points. The algorithm extends the capacity scaling approach for the submodular flow problem by Fleischer, Iwata ...