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Ravi","submitted_at":"2017-06-20T17:41:43Z","abstract_excerpt":"In the prize-collecting Steiner forest (PCSF) problem, we are given an undirected graph $G=(V,E)$, edge costs $\\{c_e\\geq 0\\}_{e\\in E}$, terminal pairs $\\{(s_i,t_i)\\}_{i=1}^k$, and penalties $\\{\\pi_i\\}_{i=1}^k$ for each terminal pair; the goal is to find a forest $F$ to minimize $c(F)+\\sum_{i: (s_i,t_i)\\text{ not connected in }F}\\pi_i$. The Steiner forest problem can be viewed as the special case where $\\pi_i=\\infty$ for all $i$. It was widely believed that the integrality gap of the natural (and well-studied) linear-programming (LP) relaxation for PCSF is at most 2. 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