Graph Balancing with Two Edge Types

TL;DR

This paper presents a simple 3/2 approximation algorithm for the NP-hard graph balancing problem with two edge types, effectively solving this specific case of makespan minimization.

Contribution

It provides the first efficient approximation algorithm with a proven ratio of 3/2 for the two-edge type graph balancing problem.

Findings

Achieved a 3/2 approximation ratio for the problem

Settled the special case of two-edge types in graph balancing

Demonstrated the problem's complexity and solution effectiveness

Abstract

In the graph balancing problem the goal is to orient a weighted undirected graph to minimize the maximum weighted in-degree. This special case of makespan minimization is NP-hard to approximate to a factor better than 3/2 even when there are only two types of edge weights. In this note we describe a simple 3/2 approximation for the graph balancing problem with two-edge types, settling this very special case of makespan minimization.