OpenAI的ChatGPT Sol仅用一个提示就提出了这个算法，展示了其强大的能力，值得一试。
This note closes the asymptotic gap for fractional online matching under edge arrivals, proving an optimal competitive ratio of $1/2+Θ(1/n)$. OpenAI's ChatGPT Sol suggested and analyzed the algorithm based on a single prompt, with the presentation refined over a few hours of discussion with the author.
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.