Charles Explorer logo
🇬🇧

On the Minimum Load Coloring Problem

Publication at Faculty of Mathematics and Physics |
2007

Abstract

Given a graph G=(V,E) with n vertices, m edges and maximum vertex degree d, the load distribution of a coloring is a pair df=(rf,bf), where rf is the number of edges with at least one end-vertex colored red and bf is the number of edges with at least one end-vertex colored blue. Our aim is to find a coloring f such that the (maximum) load, is minimized.

This problems arises in Wavelength Division Multiplexing (WDM), the technology currently in use for building optical communication networks. After proving that the general problem is NP-hard we give a polynomial time algorithm for optimal colorings of trees and show that the optimal load is at most 1/2+(d/m)log2n.

For graphs with genus g>0, we show that a coloring with load OPT(1+o(1)) can be computed in O(n+glogn)-time.