Approximating the asymmetric profitable tour. (3rd May 2012)

• Record Type: Journal Article
• Authors: Nguyen, Viet Hung; Nguyen, Thi Thu Thuy
• Is Part Of: International journal of mathematics in operational research. Volume 4:Number 3(2012)
• Page Start: 294
• Page End: 301
• Publication Date: 2012-05-03
• Subjects: approximation algorithm -- asymmetric profitable tour -- asymmetric prize collecting travelling salesman -- Held-Karp relaxation -- discrete optimisation -- operations research; Operations research -- Mathematical models -- Periodicals; Operations research -- Mathematics -- Periodicals; Decision making -- Mathematical models -- Periodicals; 658.4033
• Languages: English
• ISSNs: 1757-5850

Abstract

We study the version of the asymmetric prize collecting travelling 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 Dell'Amico et al. (1995), the authors defined it as the 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 travelling 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 (1993) algorithm for the symmetric PTP.