AI 中文总结
研究最大匹配问题的单遍半流算法近似率，证明无算法能超二分之一近似，表明朴素贪心算法最优，还通过“蓝图框架”给出构造及结果，解决了带抢占在线匹配最优竞争率的问题。
AI 中文摘要
我们证明，对于最大匹配问题，没有单遍半流算法（确定性或随机化）能实现优于二分之一的近似率。这意味着朴素贪心算法的最优性，回答了自该模型二十多年前引入以来图流文献中一个悬而未决的问题。我们的证明遵循作者之前引入的“蓝图框架”，该框架将证明半流匹配的下界简化为构造某些称为蓝图的组合对象。我们给出了蓝图的最优构造，在该框架中使用时可得出我们的半流匹配下界。我们的结果还意味着带抢占的在线匹配的最优竞争率是二分之一，同样与朴素贪心算法匹配，也解决了这个悬而未决的问题。
英文摘要
We prove that no single-pass semi-streaming algorithm (deterministic or randomized) can achieve a better-than-half approximation to the maximum matching problem. This implies the optimality of the naive greedy algorithm, answering an outstanding open question in the graph streaming literature since the introduction of the model over two decades ago. Our proof follows the "blueprint framework" introduced previously by the authors, which reduced proving lower bounds for semi-streaming matching to constructing certain combinatorial objects called blueprints. We present an optimal construction of blueprints that when used in this framework implies our semi-streaming matching lower bound. Our results also imply that the optimal competitive ratio of online matching with preemption is half, again matching the naive greedy algorithm, settling this open question as well.
Comments23 pages, 3 figures. Version 2: Fixed typos and minor language issues throughout
