A strongly polynomial algorithm for generalized flow maximization

TL;DR

This paper introduces a strongly polynomial algorithm for generalized flow maximization using a novel continuous scaling technique, improving efficiency and providing new solutions for related linear feasibility problems.

Contribution

It presents a new strongly polynomial algorithm for generalized flow maximization employing continuous scaling, a significant advancement over previous methods.

Findings

Algorithm runs in strongly polynomial time

Identifies tight arcs for contraction efficiently

Applies to linear feasibility with sparse matrices

Abstract

A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of steps, an arc can be identified that must be tight in every dual optimal solution, and thus can be contracted. As a consequence of the result, we also obtain a strongly polynomial algorithm for the linear feasibility problem with at most two nonzero entries per column in the constraint matrix.