On the approximability of the burning number

08/08/2023

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by   Anders Martinsson, et al.

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The burning number of a graph G is the smallest number b such that the vertices of G can be covered by balls of radii 0, 1, …, b-1. As computing the burning number of a graph is known to be NP-hard, even on trees, it is natural to consider polynomial time approximation algorithms for the quantity. The best known approximation factor in the literature is 3 for general graphs and 2 for trees. In this note we give a 2/(1-e^-2)+ε=2.313…-approximation algorithm for the burning number of general graphs, and a PTAS for the burning number of trees and forests. Moreover, we show that computing a (5/3-ε)-approximation of the burning number of a general graph G is NP-hard.