A graph coloring approach for channel assignment in cellular network via propositional satisfiability

Abstract

Graph Colorability Problem (GCP) is a well known NP-Complete problem consisting on finding the k minimum number of colors to paint the vertexes of a graph in such a way that two adjacent vertexes joined by an edge has always different colors. GCP is very important because it has many applications; one of the great application in cellular network is channel assignment[16]. Efficiant Channel assignment is a big challange in cellular network. Here, a cellular network is modeled as graph[12], set of channels (colors) must be assigned to cells (vertices) while avoiding interference. Since, till now there are not any known deterministic methods that can solved a GCP in a polynomial time [1]. But with the help of polynomial solvability of 3-SAT [14], we can solved GCP into polynomial time. In this paper, we transformed GCP into a 3-CNF-Satisfiability Problem [1,13]. Further, we illustrate it by one of the instance of graph coloring, the 3-colorable graph into 3-CNF-SAT. © 2011 IEEE.