{"id":"palomar/PALOMAR-2026-09-12-000002","url":"https://github.com/ykanoria/FD1d-Lean/tree/26a5b4e2fd83fa86053239e09e92af370c62f18c","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-12-000002-v2.json","repo":"https://github.com/ykanoria/FD1d-Lean","tags":["math.OC","math.PR","msc:68W27","msc:90C40","msc:60J20","online-algorithms","spatial-matching","probability"],"score":0,"title":"A Tight Upper Bound for Fully Dynamic Matching on the Line","trust":"high","domain":"math.OC","source":"palomar","authors":["Yash Kanoria"],"reviews":0,"subject":"math.OC","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-14","reactions":{},"formalized":true,"formalizes":[{"title":"Optimal fully dynamic matching on the line","identifier":"","relationship":"formalizes"}]}