Abstract
AbstractIn this paper, we consider the B-prize-collecting multicut problem in trees. In this problem, we are given a tree \(T=(V,E)\), a set of k source-sink pairs \(\mathcal {P}=\{(s_1,t_1),(s_2,t_2),\ldots , (s_k,t_k)\}\) and a profit bound B. Every edge \(e\in E\) has a cost \(c_e\), and every source-sink pair \((s_j,t_j)\in \mathcal {P}\) has a profit \(p_j\) and a penalty \(\pi _j\). This problem is to find a multicut \(M\subseteq E\) such that the total cost, which consists of the total cost of the edges in M and the total penalty of the pairs still connected after removing M, is minimized and the total profit of the disconnected pairs by removing M is at least B. Based on the primal-dual scheme, we present an \((\frac{8}{3}+ \epsilon )\)-approximation algorithm by carefully increasing the penalty, where \(\epsilon \) is any fixed positive number. KeywordsMulticut problem in treesB-prize-collectingApproximation algorithmPrimal-dual scheme
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