{
  "abstract": "This paper proposes a distributed resource allocation algorithm in which each agent communicates only the sign of its local cost gradient, a single bit per directed link per iteration. The algorithm is based on Laplacian-gradient dynamics and preserves the equality (demand) constraint at every iterate, guaranteeing anytime feasibility irrespective of termination time. First, we provide a complete Lyapunov-based convergence analysis for the fixed-step-size regime: the iterates are shown to enter, in at most O(1/\\varepsilon^2) iterations, a neighborhood of the optimizer whose radius scales as O(τ) in the decision variable and O(τ^2) in the cost residual, where $τ$ is the step-size. Crucially, the step-size bound is a time-invariant network constant (depending only on the graph Laplacian spectrum and the cost curvature bounds), so no adaptive tuning is required. Second, we characterize the invariant set under B-connected, weight-balanced digraphs, strictly weaker than the all-time connectivity and doubly-stochastic weights assumed in most prior work, and show that any odd, sign-preserving nonlinearity yields the same invariant-set and descent structure, with the single-bit protocol being the extreme communication-minimizing instance of a broader nonlinear class. Third, we address local box constraints via smooth penalty relaxation and quantify explicitly how the penalty weight interacts with the step-size bound and the optimality gap. Simulations on economic dispatch (1000 generators) and CPU scheduling (500 servers) demonstrate that the single-bit protocol achieves 5-60 times reduction in total communication cost relative to multi-bit baselines, at the price of a tunable and explicitly bounded optimality gap. A diminishing step-size schedule is shown empirically to eliminate this gap; its formal convergence analysis is identified as an open problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24431",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohammadreza Doostmohammadian"
    },
    {
      "name": "Sergio Pequito"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/09y90h5x7rp4p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24431",
  "fulltext_url": null,
  "id": "09y90h5x7rp4p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24431",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DC"
    ],
    [
      "arxiv",
      "cs.MA"
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    [
      "arxiv",
      "cs.SY"
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      "arxiv",
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      "arxiv",
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  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.24431",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/09y90h5x7rp4p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24431",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24431"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Low-Bit Distributed Constrained Optimization with Application to Optimal Scheduling and Allocation",
  "title_text": "Low-Bit Distributed Constrained Optimization with Application to Optimal Scheduling and Allocation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/09y90h5x7rp4p",
  "venue": "arXiv",
  "versions": []
}