AI 中文总结
本短文填补边到达场景下分数在线匹配的渐近界缺口，证明其最优竞争比为$1/2+\u0398(1/n)$，相关算法由OpenAI的ChatGPT Sol提出并经讨论优化。
AI 中文摘要
本短文填补了边到达场景下分数在线匹配问题已知上界与下界之间的渐近差距，证明该问题的最优竞争比为$1/2+\u0398(1/n)$。该算法由OpenAI的ChatGPT Sol基于单个提示提出并分析，经与作者数小时的反复讨论后优化呈现，作者对所有错误承担责任。
英文摘要
In this brief note, we close the asymptotic gap between known upper and lower bounds for fractional online matching under edge arrivals. We prove that the optimal competitive ratio for this problem is $1/2+Θ(1/n)$. The algorithm was suggested and analyzed by OpenAI's ChatGPT Sol based on a single prompt. The presentation was streamlined over a few hours, based on a back and forth discussion with the author, who assumes responsibility for any errors.
CommentsNote. See Section 3 (Reflections) for broader discussion on the impact of LLMs on mathematical research
