Finding a Feasible Flow in a Strongly Connected Network

TL;DR

This paper presents a simpler and faster algorithm for finding feasible flows in strongly connected networks with fixed supplies and demands, improving existing methods in terms of efficiency.

Contribution

It introduces a simpler algorithm that improves the worst-case time bound for feasible flow computation in strongly connected networks.

Findings

The new algorithm is faster than previous methods.

It simplifies the process of finding feasible flows.

The algorithm maintains correctness and efficiency.

Abstract

We consider the problem of finding a feasible single-commodity flow in a strongly connected network with fixed supplies and demands, provided that the sum of supplies equals the sum of demands and the minimum arc capacity is at least this sum. A fast algorithm for this problem improves the worst-case time bound of the Goldberg-Rao maximum flow method by a constant factor. Erlebach and Hagerup gave an linear-time feasible flow algorithm. We give an arguably simpler one.