Abstrakt
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 v0, . . ., vg-1 in V satisfying the property that for each u ELEMENT OF V there exists i ELEMENT OF {0, . . ., g - 1} so that the distance between u and vi 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.