Capacity scaling algorithm for scalable M-convex submodular flow problems

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 ...

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 dual descent algorithm for node-capacitated multiflow problems and its applications

In this paper, we develop an O((m log k)MSF(n,m, 1))-time algorithm to find a halfintegral node-capacitated multiflow of the maximum total flow-value in a network with n nodes, m edges, and k terminals, where MSF(n′,m′, γ) denotes the time complexity of solving the maximum submodular flow problem in a network with n′ edges, m′ edges, and the complexity γ of computing the exchange capacity of th...

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