Safe separators for treewidth:
Abstract: "A set of vertices S [subset of] V is called a safe separator for treewidth, if S is a separator of G, and the treewidth of G equals the maximum of the treewidth over all connected components W of G - S of the graph, obtained by making S a clique in the subgraph of G, induced by W [un...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
2003
|
| Schriftenreihe: | ZIB-Report / Konrad-Zuse-Zentrum für Informationstechnik Berlin
2003,32 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "A set of vertices S [subset of] V is called a safe separator for treewidth, if S is a separator of G, and the treewidth of G equals the maximum of the treewidth over all connected components W of G - S of the graph, obtained by making S a clique in the subgraph of G, induced by W [union of] S. We show that such safe separators are a very powerful tool for preprocessing graphs when we want to compute their treewidth. We give several sufficient conditions for separators to be safe, allowing such separators, if existing, to be found in polynomial time. In particular, every minimal separator of size one or two is safe, every minimal separator of size three that does not split off a component with only one vertex is safe, and every minimal separator that is an almost clique is safe; an almost clique is a set of vertices W such that there is a v [element of] W with W - [v] a clique. We report on experiments that show significant reductions of instance sizes for graphs from probabilistic networks and frequency assignment." |
| Beschreibung: | 19 S. graph. Darst. : 30 cm |
Internformat
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| 100 | 1 | |a Bodlaender, Hans L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Safe separators for treewidth |c Hans L. Bodlaender ; Arie M. C. A. Koster |
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| 490 | 1 | |a ZIB-Report / Konrad-Zuse-Zentrum für Informationstechnik Berlin |v 2003,32 | |
| 520 | 3 | |a Abstract: "A set of vertices S [subset of] V is called a safe separator for treewidth, if S is a separator of G, and the treewidth of G equals the maximum of the treewidth over all connected components W of G - S of the graph, obtained by making S a clique in the subgraph of G, induced by W [union of] S. We show that such safe separators are a very powerful tool for preprocessing graphs when we want to compute their treewidth. We give several sufficient conditions for separators to be safe, allowing such separators, if existing, to be found in polynomial time. In particular, every minimal separator of size one or two is safe, every minimal separator of size three that does not split off a component with only one vertex is safe, and every minimal separator that is an almost clique is safe; an almost clique is a set of vertices W such that there is a v [element of] W with W - [v] a clique. We report on experiments that show significant reductions of instance sizes for graphs from probabilistic networks and frequency assignment." | |
| 650 | 4 | |a Decomposition (Mathematics) | |
| 650 | 4 | |a Trees (Graph theory) | |
| 700 | 1 | |a Koster, Arie M. C. A. |e Verfasser |4 aut | |
| 810 | 2 | |a Konrad-Zuse-Zentrum für Informationstechnik Berlin |t ZIB-Report |v 2003,32 |w (DE-604)BV013191727 |9 2003,32 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-012766784 | ||
Datensatz im Suchindex
| _version_ | 1804132705823096832 |
|---|---|
| any_adam_object | |
| author | Bodlaender, Hans L. Koster, Arie M. C. A. |
| author_facet | Bodlaender, Hans L. Koster, Arie M. C. A. |
| author_role | aut aut |
| author_sort | Bodlaender, Hans L. |
| author_variant | h l b hl hlb a m c a k amca amcak |
| building | Verbundindex |
| bvnumber | BV017753867 |
| ctrlnum | (OCoLC)54357355 (DE-599)BVBBV017753867 |
| format | Book |
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| id | DE-604.BV017753867 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:57:04Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012766784 |
| oclc_num | 54357355 |
| open_access_boolean | |
| owner | DE-703 DE-188 |
| owner_facet | DE-703 DE-188 |
| physical | 19 S. graph. Darst. : 30 cm |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik |
| record_format | marc |
| series2 | ZIB-Report / Konrad-Zuse-Zentrum für Informationstechnik Berlin |
| spelling | Bodlaender, Hans L. Verfasser aut Safe separators for treewidth Hans L. Bodlaender ; Arie M. C. A. Koster Berlin Konrad-Zuse-Zentrum für Informationstechnik 2003 19 S. graph. Darst. : 30 cm txt rdacontent n rdamedia nc rdacarrier ZIB-Report / Konrad-Zuse-Zentrum für Informationstechnik Berlin 2003,32 Abstract: "A set of vertices S [subset of] V is called a safe separator for treewidth, if S is a separator of G, and the treewidth of G equals the maximum of the treewidth over all connected components W of G - S of the graph, obtained by making S a clique in the subgraph of G, induced by W [union of] S. We show that such safe separators are a very powerful tool for preprocessing graphs when we want to compute their treewidth. We give several sufficient conditions for separators to be safe, allowing such separators, if existing, to be found in polynomial time. In particular, every minimal separator of size one or two is safe, every minimal separator of size three that does not split off a component with only one vertex is safe, and every minimal separator that is an almost clique is safe; an almost clique is a set of vertices W such that there is a v [element of] W with W - [v] a clique. We report on experiments that show significant reductions of instance sizes for graphs from probabilistic networks and frequency assignment." Decomposition (Mathematics) Trees (Graph theory) Koster, Arie M. C. A. Verfasser aut Konrad-Zuse-Zentrum für Informationstechnik Berlin ZIB-Report 2003,32 (DE-604)BV013191727 2003,32 |
| spellingShingle | Bodlaender, Hans L. Koster, Arie M. C. A. Safe separators for treewidth Decomposition (Mathematics) Trees (Graph theory) |
| title | Safe separators for treewidth |
| title_auth | Safe separators for treewidth |
| title_exact_search | Safe separators for treewidth |
| title_full | Safe separators for treewidth Hans L. Bodlaender ; Arie M. C. A. Koster |
| title_fullStr | Safe separators for treewidth Hans L. Bodlaender ; Arie M. C. A. Koster |
| title_full_unstemmed | Safe separators for treewidth Hans L. Bodlaender ; Arie M. C. A. Koster |
| title_short | Safe separators for treewidth |
| title_sort | safe separators for treewidth |
| topic | Decomposition (Mathematics) Trees (Graph theory) |
| topic_facet | Decomposition (Mathematics) Trees (Graph theory) |
| volume_link | (DE-604)BV013191727 |
| work_keys_str_mv | AT bodlaenderhansl safeseparatorsfortreewidth AT kosterariemca safeseparatorsfortreewidth |