AI 中文总结
本文探究大语言模型（LLMs）简化算法的能力，通过评估三种LLMs在十个算法问题上的表现，发现了两种新算法，分别改进了顶点着色的非对称调色板稀疏化界定，并简化了无向图全局最小割算法。
AI 中文摘要
拥有简单的算法对新算法的实际应用至关重要。然而，简化现有算法这一领域通常很少受到理论计算机科学界的关注，且该任务似乎很适合由大语言模型（LLMs）来完成。因此，本文通过在十个不同的算法问题上评估三种不同的大语言模型（LLMs），研究了大语言模型（LLMs）简化算法的效果。研究中发现了两种新算法：第一种是针对顶点着色的算法，它以非常简单的证明对Assadi和Yazdanyar[SOSA 2025]提出的所谓非对称调色板稀疏化进行了改进界定；第二种是对Saranurak[SOSA 2021]提出的、利用扩展器确定性计算无向图全局最小割的算法的进一步简化。
英文摘要
Having simple algorithms is important for the practical adoption of new algorithms. However, simplifying existing algorithms is a field that does not usually receive a lot of attention from the theoretical computer science community. It also seems like a task that LLMs might perform well. Thus, in this paper we study how well LLMs can simplify algorithms by evaluating three different LLMs on ten different algorithmic problems. Our study resulted in the discovery of two novel algorithms. The first algorithm is for vertex coloring, and gives a refined bound for the so-called asymmetric palette sparsification proposed by Assadi and Yazdanyar [SOSA 2025] with a very simple proof. The second is a further simplification of the algorithm of Saranurak [SOSA 2021] for deterministically computing a global minimum cut in an unweighted graph using expanders.
