Balanced Submodular Flows

TL;DR

This paper introduces a new approach to the Balanced Submodular Flow Problem, providing a min-max formula, an efficient algorithm, and extensions to weighted and integer variants, advancing the understanding of submodular flow optimization.

Contribution

It presents a min-max formula and an $O(m^2)$ submodular minimization algorithm for the balanced submodular flow problem, including weighted and integer extensions.

Findings

Provided a min-max formula for the problem

Developed an $O(m^2)$ algorithm using submodular minimizations

Extended results to weighted and integer variants

Abstract

This paper examines the Balanced Submodular Flow Problem, that is the problem of finding a feasible submodular flow minimizing the difference between the flow values along the edges. A min-max formula is given to the problem and an algorithm is presented to solve it using $O(m^2)$ submodular function minimizations. Then, these result are extended to the weighted version of the problem. Finally, the Balanced Integer Submodular Flow Problem is discussed.