Burning graphs through farthest-first traversal

TL;DR

This paper presents a simple, efficient approximation algorithm for the graph burning problem, which measures graph vulnerability to contagion, demonstrating near-optimal solutions on benchmark datasets.

Contribution

Introduces the Burning Farthest-First (BFF) algorithm, a simple $O(n^3)$ approximation method with a provable factor for the NP-hard graph burning problem.

Findings

BFF runs in $O(n^3)$ steps.

BFF achieves an approximation factor of $3-2/b(G)$.

BFF produces solutions comparable to complex heuristics.

Abstract

The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify the vulnerability of a graph to contagion. This paper introduces a simple farthest-first traversal-based approximation algorithm for this problem over general graphs. We refer to this proposal as the Burning Farthest-First (BFF) algorithm. BFF runs in $O(n^3)$ steps and has an approximation factor of $3-2/b(G)$, where $b(G)$ is the size of an optimal solution. Despite its simplicity, BFF tends to generate near-optimal solutions when tested over some benchmark datasets; in fact, it returns similar solutions to those returned by much more elaborated heuristics from the literature.