APX-hardness and approximation for the k-burning number problem

Consider an information diffusion process on a graph G that starts with k>0 burnt vertices, and at each subsequent step, burns the neighbors of currently as well k other unburnt vertices. The k-burning number is minimum steps bk(G) such all vertices can be burned within steps. Note last step may have smaller than available, where them are burned. 1-burning coincides well-known burning problem, which was proposed to model spread social contagion. generalization allows us examine different worst-case contagion scenarios by varying factor k. In this paper we prove computing APX-hard, for any fixed constant We then give O((n+m)log⁡n)-time 3-approximation algorithm number, k≥1, n m edges, respectively. Finally, show even if sources given input, sequence itself NP-hard problem.