{"paper":{"title":"ALLSAT compressed with wildcards: All, or all maximum independent sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.MS"],"primary_cat":"cs.DS","authors_text":"Marcel Wild","submitted_at":"2009-01-28T09:09:36Z","abstract_excerpt":"An odd cycle cover is a vertex set whose removal makes a graph bipartite. We show that if a $k$-element odd cycle cover of a graph with w vertices is known then all $N$ maximum anticliques (= independent sets) can be generated in time $O(2^k w^3 + N w^2))$. Generating ${\\it all}\\ N'$ anticliques (maximum or not) is easier and works for arbitrary graphs in time $O(N'w^2)$. In fact the use of wildcards allows to compactly generate the anticliques in clusters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4417","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"}