{"paper":{"title":"Near-optimal Approximate Discrete and Continuous Submodular Function Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Aaron Sidford, Brian Axelrod, Yang P. Liu","submitted_at":"2019-08-31T09:09:08Z","abstract_excerpt":"In this paper we provide improved running times and oracle complexities for approximately minimizing a submodular function. Our main result is a randomized algorithm, which given any submodular function defined on $n$-elements with range $[-1, 1]$, computes an $\\epsilon$-additive approximate minimizer in $\\tilde{O}(n/\\epsilon^2)$ oracle evaluations with high probability. This improves over the $\\tilde{O}(n^{5/3}/\\epsilon^2)$ oracle evaluation algorithm of Chakrabarty \\etal~(STOC 2017) and the $\\tilde{O}(n^{3/2}/\\epsilon^2)$ oracle evaluation algorithm of Hamoudi \\etal.\n  Further, we leverage a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.00171","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.00171/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":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}