- Approximating the asymmetric profitable tour Viet Hung Nguyen(Hung.Nguyenlip6.fr) Thi Thu Thuy Nguyen(thnguyen2006gmail.com) 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, Held-Karp relaxation. Category 1: Combinatorial Optimization (Approximation Algorithms ) Category 2: Integer Programming (0-1 Programming ) Category 3: Network Optimization Citation: Download: [PDF]Entry Submitted: 12/10/2009Entry Accepted: 12/10/2009Entry Last Modified: 12/10/2009Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society.