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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 artificial intelligence (AI) to discover novel combinatorial structures that improve the limitations of efficient algorithms. Specifically, we use the LLM coding agent AlphaEvolve to study the average-case hardness for MAX-CUT and the MAX-Independent Set, as well as the worst-case approximate hardness for MAX-k-CUT. Using AlphaEvolve, we obtain near-optimal upper and lower bounds for the authentication algorithms for MAX-CUT and the MAX-Independent Set for 3- and 4-regular graphs, and discover novel gadget reductions to obtain new non-approximate results for MAX-4-CUT and MAX-3-CUT.

Takeaways, Limitations

New boundary settings for MAX-CUT and MAX-Independent Set using AlphaEvolve.
Improving the non-approximate results of MAX-4-CUT and MAX-3-CUT using AlphaEvolve.
Reduce computational costs by improving the validation process for configurations discovered through AlphaEvolve.
The MAX-4-CUT results slightly improved the state-of-the-art results, but the MAX-3-CUT results did not keep up with the existing SOTA.
Validation of candidate structures generated by AlphaEvolve is expensive (taking exponential time).
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