Constructive algorithms for the partial directed weighted improper coloring problem

Given a complete directed graph G with weights on the vertices and on the arcs, a θ-improper k-coloring is an assignment of at most k different colors to the vertices of G such that the weight of every vertex v is greater, by a given factor 1 θ , than the sum of the weights on the arcs (u, v) entering v with the tail u of the same color as v. For a given real number θ and an integer k, the Partial Directed Weigthed Improper Coloring Problem (PDWICP) is to determine the order of the largest induced subgraph G′ of G such that G′ admits a θ-improper k-coloring. This problem is motivated by a practical channel assignment application where the objective is to maximize the number of simultaneously communicating mobiles in a wireless network. We consider three constructive algorithms for the standard vertex coloring problem, and adapt them to the PDWICP. We show that they perform better than today’s phone operator systems based on decentralized channel assignment strategies such as fractional frequency reuse. Submitted: June 2015 Reviewed: December 2015 Revised: January 2016 Accepted: January 2016 Final: February 2016 Published: February 2016 Article type: Regular paper Communicated by: G. Liotta E-mail addresses: [email protected] (Alain Hertz) [email protected] (Romain Montagné) [email protected] (François Gagnon) 160 A. Hertz et al. Constructive algorithms for the PDWICP