An Ω(log n) Lower Bound for Online Matching on the Line

05/25/2021

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by   Kangning Wang, et al.

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For online matching with the line metric, we present a lower bound of Ω(log n) on the approximation ratio of any online (possibly randomized) algorithm. This beats the previous best lower bound of Ω(√(log n)) and matches the known upper bound of O(log n).