AI 中文总结
研究在线抢占式匹配问题，通过新方法证明该问题竞争比新上界0.5661，改进了之前的结果，且给出首个最优算法采用抢占时实例硬度的结果。
AI 中文摘要
我们研究在线抢占式匹配问题，其中图的边按顺序到达，算法必须通过接受或拒绝到达的边并可能丢弃先前接受的边来维持一个匹配。我们证明了该问题可达到的竞争比的一个新上界为0.5661。此界适用于任意随机算法、二分图，且允许算法输出分数解。我们的结果改进了之前由Huang等人 [SODA'19] 给出的最强上界2 - √2 ≈ 0.585。之前的硬度构造依赖于由顶点到达描述的边序列，在此序列下Huang等人展示了存在一个竞争比约为0.567（分数解为2 - √2）的非抢占式在线算法。因此，我们的硬度构造是首个表明最优算法采用抢占时实例的硬度的结果。
英文摘要
We study the online preemptive matching problem, in which the edges of a graph arrive sequentially and the algorithm must maintain a matching by accepting or rejecting arriving edges and possibly discarding previously accepted ones. We prove a new upper bound of $0.5661$ on the competitive ratio achievable for the problem. This bound applies to arbitrary randomized algorithms, bipartite graphs and if we allow the algorithm to output a fractional solution. Our result improves upon the strongest previously known upper bound of $2-\sqrt{2} \approx 0.585$, due to Huang et al. [SODA'19]. Previous hardness constructions relied on edge sequences described by vertex arrivals where each arriving vertex reveals its edges to yet unvaried vertices. Under such sequences, Huang et al. showed that there exists a non-preemptive online algorithm with competitive ratio $\sim0.567$ (or $2-\sqrt{2}$ for fractional solutions). Consequently, our hardness construction is the first result which shows hardness for instances where the optimal algorithm employs preemption.
Journal ref53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026), 128:1--128:21
DOI：10.4230/LIPIcs.ICALP.2026.128
