A Tight Upper Bound for Fully Dynamic Matching on the Line
There are `m` labeled supplies in `[0,1]`. In each period, an independent uniform demand arrives; an online policy selects one live supply, pays the distance between them, and replaces that supply by an independent uniform point. This is the one-dimensional fully dynamic model studied in Kanoria's [*Dynamic spatial matching*](https://doi.org/10.1214/25-AAP2154). That paper established a lower bound of order `log(m)/m` and an upper bound of order `log(m)^2/m`, and posed closing this logarithmic gap as an open problem. We construct a policy and show that its performance matches the prior known…
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