A Capacity Scaling Algorithm for M-convex Submodular Flow

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 ...

Core Discussion Paper 9947 a Faster Capacity Scaling Algorithm for Minimum Cost Submodular Flow

We describe an O(nh min{log U, n log n}) capacity scaling algorithm for the minimum cost submodular flow problem. Our algorithm modifies and extends the Edmonds–Karp capacity scaling algorithm for minimum cost flow to solve the minimum cost submodular flow problem. The modification entails scaling a relaxation parameter δ. Capacities are relaxed by attaching a complete directed graph with unifo...

A faster capacity scaling algorithm for minimum cost submodular flow

We describe an O(nhmin{logU, n log n}) capacity scaling algorithm for the minimum cost submodular flow problem. Our algorithm modifies and extends the Edmonds–Karp capacity scaling algorithm for minimum cost flow to solve the minimum cost submodular flow problem. The modification entails scaling a relaxation parameter δ. Capacities are relaxed by attaching a complete directed graph with uniform...

A Faster Capacity Scaling Algorithm for Minimum Cost Submodular Flow

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...