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Performance report of heuristic algorithm that cracked the largest Gset Ising problems (G81 cut=14060)

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arxiv 2505.18508 v1 pith:C7MOWV7L submitted 2025-05-24 cs.DS cond-mat.dis-nncs.ET

classification cs.DScond-mat.dis-nncs.ET
keywords algorithmheuristicproblemsbestreportcosmcutsgset
verification ladder T0 review T1 audit T2 compute T3 formal
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For the past 25 years, the Gset benchmark problems have challenged all manner of Ising and Max-Cut solvers. The largest of these problems have remained unsolved by any heuristic algorithm. In this report we provide data showing dramatically better speed and accuracy on these large sparse problems. Our newly discovered heuristic algorithm called Cosm reaches high (99.9% of best) solution quality orders of magnitude faster than the previous best heuristic solver results. Additionally, when afforded enough steps Cosm attains higher cuts than ever previously reported, specifically on instances G72 (cut=7008), G77 (cut=9940), and the 20,000-variable G81 (cut=14060). This report includes solution bitstrings so that the cuts can be independently validated. Remarkably, the new best solutions appear to be optimal. We believe the results are an early hint of disruptive opportunities for unconventional, hardware-centric approaches to algorithm discovery.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Cosm: Collective Switched Motion for Fast and Accurate Sparse Ising Optimization

    cs.CE 2026-04 accept novelty 7.5 of 10

    Cosm finds certified optimal cuts on Gset G72/G77/G81 and reduces best-known times-to-target on G61/G70 from hundreds of hours to 36–303 s via switched circular dynamics.

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