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Viet Hung Nguyen(Hung.Nguyenlip6.fr) Abstract: We study the version of the asymmetric prize collecting traveling salesman problem, where the objective is to find a directed tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. In \cite{Amico}, the authors defined it as the \textit{Profitable Tour Problem} (PTP). We present an $(1+\log(n))$approximation algorithm for the asymmetric PTP with $n$ is the vertex number. The algorithm that is based on Frieze et al.'s heuristic for the asymmetric traveling salesman problem as well as a method to round fractional solutions of a linear programming relaxation to integers (feasible solution for the original problem), represents a directed version of the Bienstock et al.'s \cite{Bienstock} algorithm for the symmetric PTP. Keywords: Asymmetric Prize Collecting Traveling Salesman, Profitable Tour Problem, approximation algorithm, HeldKarp relaxation. Category 1: Combinatorial Optimization (Approximation Algorithms ) Category 2: Integer Programming (01 Programming ) Category 3: Network Optimization Citation: Download: [PDF] Entry Submitted: 12/10/2009 Modify/Update this entry  
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