Approximation Algorithms and Lower Bounds for Graph Burning

Abstract

Graph Burning models information spreading in a given graph as a process such that in each step one node is infected (informed) and also the infection spreads to all neighbors of previously infected nodes. Formally, given a graph G = ( V, E ), possibly with edge lengths, the burning number b ( G ) is the minimum number g such that there exist nodes v 0 , . . . , v g − 1 ∈ V satisfying the property that for each u ∈ V there exists i ∈ { 0 , . . . , g − 1 } so that the distance between u and v i is at most i . We present a randomized 2 . 314-approximation algorithm for computing the burning number of a general graph, even with arbitrary edge lengths. We complement this by an approximation lower bound of 2 for the case of equal length edges, and a lower bound of 4 / 3 for the case when edges are restricted to have length 1. This improves on the previous 3-approximation algorithm and an APX-hardness result.