A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
A constant-factor approximation algorithm for the k MST problem (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
New Approximation Guarantees for Minimum-Weight k-Trees and Prize-Collecting Salesmen
SIAM Journal on Computing
Algorithms for the on-line quota traveling salesman problem
Information Processing Letters
Saving an epsilon: a 2-approximation for the k-MST problem in graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Online traveling salesman problem with deadline and advanced information
Computers and Industrial Engineering
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We study the online version of the Prize-Collecting Traveling Salesman Problem (PCTSP), a generalization of the Traveling Salesman Problem (TSP). In the TSP, the salesman has to visit a set of cities while minimizing the length of the overall tour. In the PCTSP, each city has a given weight and penalty, and the goal is to collect a given quota of the weights of the cities while minimizing the length of the tour plus the penalties of the cities not in the tour. In the online version, cities are disclosed over time. We give a 7/3-competitive algorithm for the problem, which compares with a lower bound of 2 on the competitive ratio of any deterministic algorithm. We also show how our approach can be combined with an approximation algorithm in order to obtain an O(1)-competitive algorithm that runs in polynomial time.