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

TL;DR

This paper presents a polynomial-time 2-approximation algorithm for minimizing the number of wavelengths and derives polynomial-time algorithms for computing the independence and clique numbers of this 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.

Figures (1)

• Figure 1: A set $R$ of requests in blue in a bidirected tree $T$ in black (left) ; the interference digraph ${\cal I}(R,T)$ coloured by the algorithm (middle) and optimally coloured (right).

Theorems & Definitions (45)

• Lemma 1
• proof
• Corollary 2
• Proposition 3
• Corollary 4
• proof
• Lemma 5
• proof
• Lemma 6
• proof