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

2026-03-02

AI Summary

This work addresses the wavelength assignment problem induced by the broadcast nature of filterless optical networks, modeling it as a proper coloring problem on a directed conflict graph induced by a set of requests over a bidirectional tree, with the objective of minimizing the number of wavelengths used. By leveraging graph-theoretic modeling and directed graph coloring analysis, the study presents the first polynomial-time 2-approximation algorithm for this problem. It further establishes that the problem is fixed-parameter tractable when parameterized by a fixed number of wavelengths \(k\). Additionally, the paper introduces the first polynomial-time algorithms for computing the independence number and clique number of the underlying conflict graph. The proposed approach significantly reduces wavelength usage while efficiently computing these critical graph parameters.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• wavelength assignment
• interference digraph
• broadcast effect
• filterless optical networks
• chromatic number

Innovation

• interference digraph
• wavelength assignment
• fixed-parameter tractability
• approximation algorithm
• bidirected tree