← 研踪 PaperTrailarXiv:2609.23947 · v2
Optimal analysis of Greedy for stochastic online Euclidean matching: flat torus to the rescue
首次提交 2026-09-21 07:44
版本更新 2026-11-05 03:58
雷达观测 2026-11-06 11:06
摘要
We study online metric matching with $n$ servers and $n$ requests, all sampled independently and uniformly from $[0,1]^d$. We analyze the Greedy algorithm, which matches each arriving request to its closest available server. Despite its strong empirical performance, non-trivial bounds on Greedy's competitive ratio were previously known only for $d = 1$, where it is $O(1)$-competitive [BFP23]. We prove that Greedy is $O(1)$-competitive for every fixed $d\geq3$ and has competitive ratio $Θ(\sqrt{\log n})$ for $d=2$. Our proof first analyzes Greedy on the flat torus and then transfers the resulting estimates to the cube.
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v2 · 2026-11-05 03:58 · 最新观测版本
Optimal analysis of Greedy for stochastic online Euclidean matching: flat torus to the rescue
We study online metric matching with $n$ servers and $n$ requests, all sampled independently and uniformly from $[0,1]^d$. We analyze the Greedy algorithm, which matches each arriving request to its closest available server. Despite its strong empirical performance, non-trivial bounds on Greedy's competitive ratio were previously known only for $d = 1$, where it is $O(1)$-competitive [BFP23]. We prove that Greedy is $O(1)$-competitive for every fixed $d\geq3$ and has competitive ratio $Θ(\sqrt{\log n})$ for $d=2$. Our proof first analyzes Greedy on the flat torus and then transfers the resulting estimates to the cube.
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