Colouring the interference digraph of a set of requests in a bidirected tree

TL;DR

This paper models the wavelength assignment problem in optical networks using an interference digraph and presents algorithms for approximation, fixed-parameter tractability, and key graph parameters.

Contribution

It introduces a novel interference digraph model for wavelength assignment and provides new polynomial-time and fixed-parameter algorithms for related problems.

Findings

A polynomial-time 2-approximation algorithm for wavelength minimization.

The problem is fixed-parameter tractable with respect to the number of wavelengths.

Polynomial algorithms for independence and clique numbers of the interference digraph.

Abstract

In this paper, we investigate the impact of the broadcast effect arising in filterless optical networks on the computational complexity of the wavelength assignment problem. We model conflicts using an appropriate interference digraph, whose proper colourings correspond to feasible wavelength assignments. Minimizing the number of required wavelengths therefore amounts to determining the chromatic number of this interference digraph. Within this framework, we first present a polynomial-time 2-approximation algorithm for minimizing the number of wavelengths. We then show that the problem is fixed-parameter tractable when parameterized by the number $k$ of available wavelengths. We also derive polynomial-time algorithms for computing the independence and clique numbers of this interference digraph.