{"paper":{"title":"Adaptive Threshold-Driven Continuous Greedy Method for Scalable Submodular Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"ATCG matches full continuous greedy objective values while bounding communication via adaptive active-set gating.","cross_cats":["math.CO"],"primary_cat":"cs.LG","authors_text":"Mohammadreza Rostami, Solmaz S. Kia","submitted_at":"2026-04-03T19:32:39Z","abstract_excerpt":"Submodular maximization under matroid constraints is a fundamental problem in combinatorial optimization with applications in sensing, data summarization, active learning, and resource allocation. While the Sequential Greedy (SG) algorithm achieves only a $\\frac{1}{2}$-approximation due to irrevocable selections, Continuous Greedy (CG) attains the optimal $\\bigl(1-\\frac{1}{e}\\bigr)$-approximation via the multilinear relaxation, at the cost of a progressively dense decision vector that forces agents to exchange feature embeddings for nearly every ground-set element. We propose \\textit{ATCG} (\\u"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"ATCG achieves objective values comparable to those of the full CG method while substantially reducing communication overhead through adaptive active-set expansion, with a curvature-aware approximation guarantee τ_eff = max{τ, 1-c}.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the per-partition progress ratio η_i can be chosen so that gating gradient evaluations does not cause the captured marginal gains to fall below the level needed for the stated approximation factor to hold.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"ATCG adaptively thresholds continuous greedy updates to limit communication in distributed submodular maximization under matroid constraints while retaining a curvature-aware approximation guarantee.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"ATCG matches full continuous greedy objective values while bounding communication via adaptive active-set gating.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"612f9f2feaaf1b2262cd5673094f745f1ce9970462c257feda722d5878c4a50b"},"source":{"id":"2604.03419","kind":"arxiv","version":2},"verdict":{"id":"1e64d2c9-a598-4ba1-a4e0-5515fda3d156","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T19:48:07.962229Z","strongest_claim":"ATCG achieves objective values comparable to those of the full CG method while substantially reducing communication overhead through adaptive active-set expansion, with a curvature-aware approximation guarantee τ_eff = max{τ, 1-c}.","one_line_summary":"ATCG adaptively thresholds continuous greedy updates to limit communication in distributed submodular maximization under matroid constraints while retaining a curvature-aware approximation guarantee.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the per-partition progress ratio η_i can be chosen so that gating gradient evaluations does not cause the captured marginal gains to fall below the level needed for the stated approximation factor to hold.","pith_extraction_headline":"ATCG matches full continuous greedy objective values while bounding communication via adaptive active-set gating."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.03419/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"0d91355411ef257f93d90a3b60357118fc0be759a971b832a57a0590c8571f19"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}