2-Coloring Cycles in One Round
Maxime Flin, Alesya Raevskaya, Ronja Stimpert, Jukka Suomela, Qingxin Yang

TL;DR
This paper presents new bounds for one-round randomized algorithms to 2-color cycles, achieving a lower expected monochromatic edge fraction than previous bounds, with proofs developed using language models and formalized in Lean 4.
Contribution
It introduces improved upper and lower bounds for one-round 2-coloring of cycles, utilizing language models and formal verification.
Findings
Expected monochromatic edges less than 0.24118 with a new algorithm
Lower bound of 0.23879 for any one-round algorithm
Previous bounds were 0.25 and 0.2
Abstract
We show that there is a one-round randomized distributed algorithm that can 2-color cycles such that the expected fraction of monochromatic edges is less than 0.24118. We also show that a one-round algorithm cannot achieve a fraction less than 0.23879. Before this work, the best upper and lower bounds were 0.25 and 0.2. Our proof was largely discovered and developed by large language models, and both the upper and lower bounds have been formalized in Lean 4.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComplexity and Algorithms in Graphs · Advanced Graph Theory Research · Constraint Satisfaction and Optimization
