{"paper":{"title":"Volume computation for sparse boolean quadric relaxations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daphne Skipper, Jon Lee","submitted_at":"2017-03-04T00:08:34Z","abstract_excerpt":"Motivated by understanding the quality of tractable convex relaxations of intractable polytopes, Ko et al. gave a closed-form expression for the volume of a standard relaxation $\\mathscr{Q}(G)$ of the boolean quadric polytope (also known as the (full) correlation polytope) $\\mathscr{P}(G)$ of the complete graph $G=K_n$. We extend this work to structured sparse graphs, giving: (i) an efficient algorithm for $vol(\\mathscr{Q}(G))$ when $G$ has bounded tree width, (ii) closed-form expressions (and asymptotic behaviors) for $vol(\\mathscr{Q}(G))$ for all stars, paths, and cycles, and (iii) a closed-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02444","kind":"arxiv","version":4},"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"}