Problem
Research questions and friction points this paper is trying to address.
asymptotic gap
fractional online matching
edge arrivals
Asymptotically Tight Fractional Online Matching Under Edge Arrivals
🤖 AI Summary
本文解决了边到达情况下的分数在线匹配问题，通过算法证明了最优竞争比为1/2+Θ(1/n)，缩小了已知上下界之间的渐近差距。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
fractional online matching
edge arrivals
competitive ratio
algorithmic proof
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2024-02-20arXiv.orgCitations: 0
