 
Summary: Coloring Graphs to Minimize Load
 Extended Abstract 
Nitin Ahuja
Andreas Baltz
Benjamin Doerr
Ales Pr´ivetiv´y §
Anand Srivastav
Abstract
Given a graph G = (V, E) with n vertices, m edges and maximum
vertex degree , the load distribution of a coloring : V {red, blue}
is a pair d = (r, b), where r is the number of edges with at least
one endvertex colored red and b is the number of edges with at least
one endvertex colored blue. Our aim is to find a coloring such that
the (maximum) load, l := max{r, b}, is minimized. The problem has
applications in broadcast WDM communication networks (Ageev et al.,
2004). After proving that the general problem is NPhard we give a
polynomial time algorithm for optimal colorings of trees and show that
the optimal load is at most m/2 + log2 n. For graphs with genus g >
0, we show that a coloring with load OPT(1 + o(1)) can be computed
in O(n + g)time, if the maximum degree satisfies = o(m2
