{
  "abstract": "Ground-state search in two-dimensional Ising spin glasses on large toroidal lattices remains challenging for local-update heuristics because rugged energy barriers impede relaxation across metastable states. Equivalent to zero-field toroidal Max-Cut problems, these spin-glass instances also serve as standard benchmarks for optimization heuristics. Many Monte Carlo approaches combine single-spin flips or cluster moves with temperature ladders or annealing schedules, yet even with tuned parameters, rarely achieve rapid, reliable ground-state convergence at scale. Here, we address the need for faster ground-state search through cooperation between replicas. We introduce ranked greedy cluster exchange (RGCX) and combine it with fixed-temperature Metropolis sweeps to form single-temperature RGCX. Replicas are ranked by cut to determine the pair-processing order. Each pair deterministically exchanges every disagreement cluster that raises the better replica's cut, retaining the complement and conserving the pair's summed cut. On the 20,000-spin Gset instance G81, the estimated runtime to reach the certified optimum with 99% success probability (TTS99) was 12.1 s on an 8-core desktop computer. With the same population size, exchange interval and temperature, the method reached the best known cuts on all 17 toroidal Gset graphs, including 9 certified optima. These findings advance ground-state search on large two-dimensional tori by establishing single-temperature RGCX as an efficient population-based method that combines ranked greedy cluster exchange with fixed-temperature Metropolis dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40515",
  "author_total": 3,
  "authors": [
    {
      "name": "Hao Geng"
    },
    {
      "name": "Nan Su"
    },
    {
      "name": "Gabriele Cavallaro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4vm71fw2ab5xm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40515",
  "fulltext_url": null,
  "id": "4vm71fw2ab5xm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40515",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "hep-lat"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40515",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4vm71fw2ab5xm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40515",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40515"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    }
  ],
  "title": "Single-Temperature Ranked Greedy Cluster Exchange for Max-Cut on Two-Dimensional Tori",
  "title_text": "Single-Temperature Ranked Greedy Cluster Exchange for Max-Cut on Two-Dimensional Tori",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/4vm71fw2ab5xm",
  "venue": "arXiv",
  "versions": []
}