Online traveling salesman problems with rejection options
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Jaillet_online-tsp-rejections-final.pdf
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334.71 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
Jaillet, Patrick
Lu, Xin
Xin, Lu
Date Issued
August 2014
Journal
Networks
Publisher
Wiley Blackwell
Citation
Jaillet, Patrick, and Xin Lu. “Online Traveling Salesman Problems with Rejection Options.” Networks 64, no. 2 (August 11, 2014): 84–95.
Version
Author's final manuscript
Abstract
In this article, we consider online versions of the traveling salesman problem on metric spaces for which requests to visit points are not mandatory. Associated with each request is a penalty (if rejected). Requests are revealed over time (at their release dates) to a server who must decide which requests to accept and serve in order to minimize a linear combination of the time to serve all accepted requests and the total penalties of all rejected requests. In the basic online version of the problem, a request can be accepted any time after its release date. In the real-time online version, a request must be accepted or rejected at the time of its release date. For the basic version, we provide a best possible 2-competitive online algorithm for the problem on a general metric space. For the real-time version, we first consider special metric spaces: on the nonnegative real line, we provide a best possible 2.5-competitive polynomial time online algorithm; on the real line, we prove a Ω(√ln n) lower bound of 2.64 on any competitive ratios and give a 3-competitive online algorithm. We then consider the case of a general metric space and prove a inline image lower bound on the competitive ratio of any online algorithms. Finally, among the restricted class of online algorithms with prior knowledge about the total number of requests n, we propose an asymptotically best possible O(√ln n)-competitive algorithm.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Massachusetts Institute of Technology. Operations Research Center
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Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1002/net.21559
