Daily Arxiv

This page organizes papers related to artificial intelligence published around the world.
This page is summarized using Google Gemini and is operated on a non-profit basis.
The copyright of the paper belongs to the author and the relevant institution. When sharing, simply cite the source.

Reinforced Generation of Combinatorial Structures: Applications to Complexity Theory

Created by
  • Haebom

Author

Ansh Nagda, Prabhakar Raghavan, Abhradeep Thakurta

Outline

This paper explores the use of AI technology to discover novel combinatorial structures that improve existing limitations of efficient algorithms. Specifically, we use AlphaEvolve (an LLM coding agent) to study the average case hardness for MAX-CUT and MAX-Independent Sets, as well as the worst-case approximate hardness for MAX-k-CUT. Through this, we improve the upper and lower bounds of the authentication algorithm for MAX-CUT and MAX-Independent Sets, and obtain new non-approximate probability results for MAX-4-CUT and MAX-3-CUT. Furthermore, we propose a method for efficiently improving the verification process using AlphaEvolve.

Takeaways, Limitations

Takeaways:
Leveraging AI technology (AlphaEvolve) to produce new results that push the boundaries of existing algorithms.
Boundary improvements for MAX-CUT and MAX-Independent Set.
We present new non-approximate feasibility results for MAX-4-CUT and MAX-3-CUT.
Provide criteria for evaluating how AI contributes to proof development.
Limitations:
It takes a significant amount of time to verify the results generated by AlphaEvolve.
MAX-3-CUT results are below best performance (compared to custom PCP method).
👍