SWAT 2006: Algorithm Theory – SWAT 2006 pp 423-434

Generalized Powers of Graphs and Their Algorithmic Use

• Andreas Brandstädt
• Feodor F. Dragan
• Yang Xiang
• Chenyu Yan
Conference paper

DOI: 10.1007/11785293_39

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4059)
Cite this paper as:
Brandstädt A., Dragan F.F., Xiang Y., Yan C. (2006) Generalized Powers of Graphs and Their Algorithmic Use. In: Arge L., Freivalds R. (eds) Algorithm Theory – SWAT 2006. SWAT 2006. Lecture Notes in Computer Science, vol 4059. Springer, Berlin, Heidelberg

Abstract

Motivated by the frequency assignment problem in heterogeneous multihop radio networks, where different radio stations may have different transmission ranges, we introduce two new types of coloring of graphs, which generalize the well-known Distance-k-Coloring. Let G=(V,E) be a graph modeling a radio network, and assume that each vertex v of G has its own transmission radius r(v), a non-negative integer. We define r-coloring (r + -coloring) of G as an assignment Φ: V↦{0,1,2,...} of colors to vertices such that Φ(u)=Φ(v) implies dG(u,v)>r(v)+r(u) (dG(u,v)>r(v)+r(u)+1, respectively). The r-Coloring problem (the r + -Coloring problem) asks for a given graph G and a radius-function r: VN∪{0}, to find an r-coloring (an r + -coloring, respectively) of G with minimum number of colors. Using a new notion of generalized powers of graphs, we investigate the complexity of the r-Coloring and r + -Coloring problems on several families of graphs.

Authors and Affiliations

• Andreas Brandstädt
• 1
• Feodor F. Dragan
• 2
• Yang Xiang
• 2
• Chenyu Yan
• 2
1. 1.FB InformatikUniversität RostockRostockGermany
2. 2.Department of Computer ScienceKent State UniversityKentUSA