Can LLMs be Used to Simplify Algorithms? Simpler Algorithms for Vertex Coloring and Edge Connectivity

2026-08-11

AI Summary

Algorithm simplification has long lacked systematic investigation, hindering the practical deployment of complex algorithms. This work presents the first systematic exploration of the potential of large language models (LLMs) in algorithm simplification, leveraging the analytical framework of graph algorithms from theoretical computer science to evaluate three LLMs across ten classical algorithmic problems. The study successfully generates two novel algorithms that are both simpler and more interpretable while preserving theoretical performance guarantees: an improved vertex coloring algorithm for asymmetric palette sparsification accompanied by a concise correctness proof, and a further simplified deterministic algorithm for global minimum cut in unweighted graphs based on expander decompositions. These results demonstrate that LLMs can effectively enhance algorithmic understandability and practical utility.

Abstract

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.

Problem

• algorithm simplification
• large language models
• vertex coloring
• edge connectivity
• practical algorithm design

Innovation

• algorithm simplification
• large language models
• vertex coloring
• edge connectivity
• expander graphs