Prize-Collecting Steiner Network Problems

In the Steiner Network problem we are given a graph with edge-costs and connectivity requirements between node pairs , . The goal is to find a minimum-cost subgraph of that contains edge-disjoint paths for all , . In Prize-Collecting Steiner Network problems we do not need to satisfy all requirements, but are given a penalty function for violating the connectivity requirements, and the goal is to find a subgraph that minimizes the cost plus the penalty. The case when {0, 1} is the classic Prize-Collecting Steiner Forest problem. In this paper we present a novel linear programming relaxation for the Prize-Collecting Steiner Network problem, and by rounding it, obtain the first constant-factor approximation algorithm for submodular and monotone non-decreasing penalty functions. In particular, our setting includes all-or-nothing penalty functions, which charge the penalty even if the connectivity requirement is slightly violated; this resolves an open question posed in [SSW07]. We furth...

• Type: Conference
• Year: 2010
• Where: IPCO
• Authors: MohammadTaghi Hajiaghayi, Rohit Khandekar, Guy Kortsarz, Zeev Nutov
• Keywords: Connectivity Requirement, IPCO 2010, Optimization, Penalty Functions, Steiner Network Problem