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Coloring Graphs to Minimize Load -Extended Abstract -
 

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 end-vertex colored red and b is the number of edges with at least
one end-vertex 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 NP-hard 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

  

Source: Ahuja, Nitin - Fachbereich Mathematik und Informatik, Technische Universität Braunschweig

 

Collections: Mathematics