Abstract
We introduce the online bottleneck semi-matching (OBSM) problem, which is to assign a sequence of requests to a given set of m servers, such that the maximum cost is minimized. We present a lower bound \(m+1\) and an online algorithm with competitive ratio \(2m-1\) for the OBSM problem on a line, where the distance between every pair of adjacent servers is the same. When \(m=2\), we present an optimal online algorithm with competitive ratio 3 for the OBSM problem. When \(m=3\), we present two optimal online algorithms with competitive ratio at most \(3+\sqrt{2}\) for the OBSM problem on a line, which matches the previous best lower bound proposed about thirty years ago.
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Acknowledgement
The work is supported in part by the National Natural Science Foundation of China [No. 12071417], Program for Excellent Young Talents of Yunnan University, Training Program of National Science Fund for Distinguished Young Scholars, and IRTSTYN.
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Xiao, M., Zhao, S., Li, W., Yang, J. (2021). Online Bottleneck Semi-matching. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_35
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DOI: https://doi.org/10.1007/978-3-030-92681-6_35
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