Yet another approach to the Maximum Flow

TL;DR

This paper presents a new maximum flow algorithm based on arc sorting that improves runtime to O(mn^0.5), offering a simpler method with better efficiency for network flow problems.

Contribution

Introduces a novel maximum flow algorithm utilizing arc sorting, achieving a faster runtime of O(mn^0.5) for certain network types.

Findings

Achieves an O(mn^0.5) time complexity for maximum flow.

Simplifies the maximum flow algorithm using arc sorting.

Provides potential improvements over existing algorithms.

Abstract

I introduce a new approach to the maximum flow problem by a simple algorithm with a slightly better runtime. This approach is based on sorting arcs insight of vertices on a residual graph. This new approach leads to an O(mn^0.5) time bound for a network with n vertices and m arcs. Category: Algorithms, Graph Theory and maximum flows