We present a simple proof that no randomized online matching algorithm for the line can be \((\sqrt {\log _2(n+1)}/15)\)-competitive against an oblivious adversary for any n = 2ⁱ - 1 : i ∈ ℕ. This is the first super-constant lower bound for the problem, and disproves as a corollary a recent conjecture on the topology-parametrized competitiveness achievable on generic spaces.

中文翻译：

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线上匹配不承认 \(o(\sqrt {\log n})\) -竞争算法

我们提出了一个简单的证明，即对于任何n = 2，没有任何随机在线匹配算法可以与不经意的对手竞争 \((\sqrt {\log _2(n+1)}/15)\)ⁱ - 1 : i ∈ ℕ。这是该问题的第一个超常数下界，并作为推论反驳了最近关于在泛型空间上可实现的拓扑参数化竞争力的猜想。