An approximation algorithm for the k-prize-collecting hitting set problem

We study the k-prize-collecting hitting set problem in hypergraphs. We first design a greedy algorithm for the k-hitting set problem with approximation ratio \(\min \{k,\Delta \}\) $min\{k,\mathrm{\Delta }\}$ , where \({\Delta}\) $\mathrm{\Delta }$ is the maximum degree of all vertices in the hypergraph. Then we design an LP-rounding algorithm for the prize-collecting hitting set problem with approximation ratio \({l+1}\) $l+1$ , where l is the maximum size of all hyperedges. As a result, we obtain an \((l+1+\min \{k,\Delta \})\) $(l+1+min\{k,\mathrm{\Delta }\})$ -approximation algorithm for the k-prize-collecting hitting set problem based on the two algorithms mentioned above.