{"paper":{"title":"On graph classes with logarithmic boolean-width","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Martin Vatshelle, R\\'emy Belmonte","submitted_at":"2010-09-01T16:06:00Z","abstract_excerpt":"Boolean-width is a recently introduced graph parameter. Many problems are fixed parameter tractable when parametrized by boolean-width, for instance \"Minimum Weighted Dominating Set\" (MWDS) problem can be solved in $O^*(2^{3k})$ time given a boolean-decomposition of width $k$, hence for all graph classes where a boolean-decomposition of width $O(\\log n)$ can be found in polynomial time, MWDS can be solved in polynomial time. We study graph classes having boolean-width $O(\\log n)$ and problems solvable in $O^*(2^{O(k)})$, combining these two results to design polynomial algorithms. We show that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0216","kind":"arxiv","version":2},"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"}