Topological Interference Management with Adversarial Topology Perturbation: An Algorithmic Perspective

TL;DR

This paper addresses the topological interference management problem in dynamic networks by proposing a graph coloring algorithm that maintains optimality under adversarial topology perturbations, specifically for chordal networks.

Contribution

It introduces a dynamic graph coloring algorithm that minimizes re-coloring updates to counter adversarial topology changes in chordal networks, achieving optimal interference management.

Findings

The algorithm requires only a constant number of re-coloring updates per edge change.

It exploits structural properties of chordal graphs for efficiency.

The approach achieves information-theoretic optimality under adversarial perturbations.

Abstract

In this paper, we consider the topological interference management (TIM) problem in a dynamic setting, where an adversary perturbs network topology to prevent the exploitation of sophisticated coding opportunities (e.g., interference alignment). Focusing on a special class of network topology - chordal networks - we investigate algorithmic aspects of the TIM problem under adversarial topology perturbation. In particular, given the adversarial perturbation with respect to edge insertion/deletion, we propose a dynamic graph coloring algorithm that allows for a constant number of re-coloring updates against each inserted/deleted edge to achieve the information-theoretic optimality. This is a sharp reduction of the general graph re-coloring, whose optimal number of updates scales as the size of the network, thanks to the delicate exploitation of the structural properties of chordal graph classes.