{"paper":{"title":"Fast Dynamic Programming on Graph Decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Erik Jan van Leeuwen, Hans L. Bodlaender, Johan M. M. Van Rooij, Martin Vatshelle, Peter Rossmanith","submitted_at":"2018-06-05T13:02:35Z","abstract_excerpt":"In this paper, we consider tree decompositions, branch decompositions, and clique decompositions. We improve the running time of dynamic programming algorithms on these graph decompositions for a large number of problems as a function of the treewidth, branchwidth, or cliquewidth, respectively.\n  On tree decompositions of width $k$, we improve the running time for Dominating Set to $O(3^k)$. We generalise this result to $[\\rho,\\sigma]$-domination problems with finite or cofinite $\\rho$ and $\\sigma$. For these problems, we give $O(s^k)$-time algorithms, where $s$ is the number of `states' a ver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01667","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"}