On the Minimum Load Coloring Problem

Given a graph G = (V, E) with n vertices, m edges and maximum vertex degree ∆, the load distribution of a coloring ϕ : V → {red, blue} is a pair dϕ = (rϕ, bϕ), where rϕ is the number of edges with at least one end-vertex colored red and bϕ is the number of edges with at least one end-vertex colored blue. Our aim is to find a coloring ϕ such that the (maximum) load, lϕ := 1 m · max{rϕ, bϕ}, 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+(∆/m) 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 log n)-time, if the maximum degree satisfies ∆ = o(m2 ng ) and an embedding is given. In the general situation we show that a coloring with load a...

• Type: Conference
• Year: 2005
• Where: WAOA
• Authors: Nitin Ahuja, Andreas Baltz, Benjamin Doerr, Ales Prívetivý, Anand Srivastav
• Keywords: Load Distribution, Maximum Vertex Degree, Optimal Load, WAOA 2005