{"paper":{"title":"Algorithmic Meta-Theorems for Monotone Submodular Maximization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Masakazu Ishihata, Takanori Maehara, Tomas Rigaux","submitted_at":"2018-07-12T12:36:27Z","abstract_excerpt":"We consider a monotone submodular maximization problem whose constraint is described by a logic formula on a graph. Formally, we prove the following three `algorithmic metatheorems.'\n  (1) If the constraint is specified by a monadic second-order logic on a graph of bounded treewidth, the problem is solved in $n^{O(1)}$ time with an approximation factor of $O(\\log n)$.\n  (2) If the constraint is specified by a first-order logic on a graph of low degree, the problem is solved in $O(n^{1 + \\epsilon})$ time for any $\\epsilon > 0$ with an approximation factor of $2$.\n  (3) If the constraint is spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04575","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":""},"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"}