Approximating the asymmetric profitable tour

Viet Hung Nguyen and Thi Thu Thuy Nguyen

International Journal of Mathematics in Operational Research, 2012, vol. 4, issue 3, 294-301

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.

Keywords: approximation algorithms; asymmetric profitable tour; asymmetric prize collecting TSP; travelling salesman problem; Held-Karp relaxation; discrete optimisation; operations research. (search for similar items in EconPapers)
Date: 2012
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