{"paper":{"title":"On the Equivalence among Problems of Bounded Width","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Yoichi Iwata, Yuichi Yoshida","submitted_at":"2015-09-03T09:58:50Z","abstract_excerpt":"In this paper, we introduce a methodology, called decomposition-based reductions, for showing the equivalence among various problems of bounded-width.\n  First, we show that the following are equivalent for any $\\alpha > 0$:\n  * SAT can be solved in $O^*(2^{\\alpha \\mathrm{tw}})$ time,\n  * 3-SAT can be solved in $O^*(2^{\\alpha \\mathrm{tw}})$ time,\n  * Max 2-SAT can be solved in $O^*(2^{\\alpha \\mathrm{tw}})$ time,\n  * Independent Set can be solved in $O^*(2^{\\alpha \\mathrm{tw}})$ time, and\n  * Independent Set can be solved in $O^*(2^{\\alpha \\mathrm{cw}})$ time, where tw and cw are the tree-width "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01014","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"}