We revisit the fully online matching model (Huang et al., J.\ ACM, 2020), an extension of the classic online matching model due to Karp, Vazirani, and Vazirani (STOC 1990), which has recently received a lot of attention (Huang et al., SODA 2019 and FOCS 2020), partly due to applications in ride-sharing platforms. It has been shown that the fully online version is harder than the classic version for which the achievable competitive ratio is at most $0.6317$, rather than precisely $1-\frac{1}{e}\approx 0.6321$. We introduce two new ideas to the construction. By optimizing the parameters of the modified construction numerically, we obtain an improved impossibility result of $0.6297$. Like the previous bound, the new bound even holds for fractional (rather than randomized) algorithms on bipartite graphs.
翻译：我们重新审视了完全在线匹配模式(Huang等人,J.\ ACM,2020年),这是Karp、Vazirani和Vazirani(STOC,1990年)的经典在线匹配模式的延伸,后者最近受到极大关注(Huang等人,SODA 2019和FOCS 2020年),部分是由于在搭载平台上的应用。我们发现,完全在线版本比经典版本更难,其可实现的竞争比率最高为0.6317美元,而不是精确地说1美元-frac{1 ⁇ ⁇ ⁇ approx 0.6321美元。我们为该建筑引入了两个新理念。通过从数字上优化修改后的建筑参数,我们获得了0.6297美元的改进的不可能结果。和以往的结合一样,新的约束甚至维持了双方图上的分数(而不是随机)算法。
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