New heuristics for burning graphs

TL;DR

This paper introduces new heuristics for approximating the graph burning number, an NP-complete problem modeling contagion spread, and evaluates their performance on various graph classes and benchmarks.

Contribution

The paper develops the first heuristics for solving the graph burning problem in general graphs and improves upper bounds based on graph clustering.

Findings

Heuristics perform well on benchmark graphs and random graphs.

Improved upper bounds for burning number based on distance to cluster.

Heuristics provide practical solutions for NP-hard graph burning problem.

Abstract

The concept of graph burning and burning number ($bn(G)$) of a graph G was introduced recently [1]. Graph burning models the spread of contagion (fire) in a graph in discrete time steps. $bn(G)$ is the minimum time needed to burn a graph $G$.The problem is NP-complete. In this paper, we develop first heuristics to solve the problem in general (connected) graphs. In order to test the performance of our algorithms, we applied them on some graph classes with known burning number such as theta graphs, we tested our algorithms on DIMACS and BHOSLIB that are known benchmarks for NP-hard problems in graph theory. We also improved the upper bound for burning number on general graphs in terms of their distance to cluster. Then we generated a data set of 2000 random graphs with known distance to cluster and tested our heuristics on them.