Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 3 2 2022 09 01 New heuristics for burning connected graphs 165 172 4911 10.22060/ajmc.2022.21692.1101 EN Maryam Tahmasbi Department of Computer and Data Sciences, Shahid Beheshti University, Tehran, Iran Zahra Rezai Farokh Department of Computer and Data Sciences, Shahid Beheshti University, Tehran, Iran Yousof Buali Department of Computer and Data Sciences, Shahid Beheshti University, Tehran, Iran Zahra Haj Rajab Ali Tehrani Department of Computer and Data Sciences, Shahid Beheshti University, Tehran, Iran Journal Article 2022 08 20 The concept of graph burning and burning number $(bn(G))$ of a graph $G$ was introduced recently [4]. 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 1000 random graphs with known distance to cluster and tested our heuristics on them. https://ajmc.aut.ac.ir/article_4911_68abef8ee1ac9b664a90b0bbaff4f770.pdf