边到达概率消失时的在线匹配与争议解决

我们研究了在边概率消失的随机图上进行的顺序争议解决和匹配算法的性能。当图的边以对抗性选择的顺序处理时，我们推导出一种新的OCR（争议解决算法），其可选取性为0.382，达到了文献中在边概率消失假设下的"独立基准"。complementary to this positive result, we show that no OCR can be more than 0.390-selectable, significantly improving upon the upper bound of 0.428 from the literature. 我们也推导出针对二分图或OCR子族的负结果。同时，当图的边以均匀随机的顺序处理时，我们表明简单的贪心争议解决方案——接受所有活跃且可行的边——是1/2可选的。该结果是紧致的，由于已知的上界。最终，当算法可以选择处理顺序时，我们表明稍微调整后的随机顺序——为每个顶点分配随机优先级并按字典序处理边—— resulting in a strictly better contention resolution scheme that is $1-\ln(2-1/e)\approx0.510$-selectable. Our positive results also apply to online matching on $1$-uniform random graphs with vanishing (non-identical) edge probabilities, extending and unifying some results from the random graphs literature.