Graph Balancing with Two Edge Types

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.

Remark. (added 9th June, 2016.) After posting the version 1 of our paper, it was brought to our notice that our result is not new. Huang and Ott [HO15], and independently, Page and Solis-Oba [PSO16] also obtain the same result