Abstract
We study a generalization of the well-known traveling salesman problem in a metric space, in which each city is associated with a release time. The salesman has to visit each city at or after its release time. There exists a naive 5/2-approximation algorithm where the salesman simply starts to route the network after all cities are released. Interestingly, this bound has never been improved for more than two decades. In this paper, we revisit the problem and achieve the following results. First, we devise an approximation algorithm with performance ratio less than 5/2 when the number of distinct release times is fixed. Then, we analyze a natural class of algorithms and show that no performance ratio better than 5/2 is possible unless the Metric TSP can be approximated with a ratio strictly less than 3/2, which is a well-known longstanding open question. Finally, we consider a special case where the graph has a heavy edge and present an approximation algorithm with performance ratio less than 5/2.
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Acknowledgements
The authors greatly appreciate the two anonymous referees for their insightful comments that help improve the presentation of this paper. The research is supported in part by the National Natural Science Foundation of China (11531014, 11671135) and the Natural Science Foundation of Shanghai (19ZR1411800).
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An extended abstract appeared in Proceedings of the 23rd International Symposium on Algorithms and Computation (Yu et al. 2012).
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Yu, W., Golin, M. & Zhang, G. Scheduling on a graph with release times. J Sched 26, 571–580 (2023). https://doi.org/10.1007/s10951-021-00680-z
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DOI: https://doi.org/10.1007/s10951-021-00680-z