Contraction and treewidth lower bounds:
Abstract: "Edge contraction is shown to be a useful mechanism to improve lower bound heuristics for treewidth. A successful lower bound for treewidth is the degeneracy: the maximum over all subgraphs of the minimum degree. The degeneracy is polynomial time computable. We introduce the notion of...
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| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
2004
|
| Schriftenreihe: | ZIB-Report
2004,29 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "Edge contraction is shown to be a useful mechanism to improve lower bound heuristics for treewidth. A successful lower bound for treewidth is the degeneracy: the maximum over all subgraphs of the minimum degree. The degeneracy is polynomial time computable. We introduce the notion of contraction degeneracy: the maximum over all minors of the minimum degree. We show that the contraction degeneracy problem is NP-complete, even for bipartite graphs, but for fixed k, it is polynomial time decidable if a given graph G has contraction degeneracy at least k. Heuristics for computing the contraction degeneracy are proposed and evaluated. It is shown that these can lead in practice to considerable improvements of the lower bound for treewidth, but can perform arbitrarily bad on some examples. A study is also made for the combination of contraction with Lucena's lower bound based on Maximum Cardinality Search [23]. Finally, heuristics for the treewidth are proposed and evaluated that combine contraction with a treewidth lower bound technique by Clautiaux et al. [12]." |
| Beschreibung: | 33 S. graph. Darst. |
Internformat
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| 100 | 1 | |a Bodlaender, Hans L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Contraction and treewidth lower bounds |c Hans L. Bodlaender ; Arie M. C. A. Koster ; Thomas Wolle |
| 264 | 1 | |a Berlin |b Konrad-Zuse-Zentrum für Informationstechnik |c 2004 | |
| 300 | |a 33 S. |b graph. Darst. | ||
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| 490 | 1 | |a ZIB-Report |v 2004,29 | |
| 520 | 3 | |a Abstract: "Edge contraction is shown to be a useful mechanism to improve lower bound heuristics for treewidth. A successful lower bound for treewidth is the degeneracy: the maximum over all subgraphs of the minimum degree. The degeneracy is polynomial time computable. We introduce the notion of contraction degeneracy: the maximum over all minors of the minimum degree. We show that the contraction degeneracy problem is NP-complete, even for bipartite graphs, but for fixed k, it is polynomial time decidable if a given graph G has contraction degeneracy at least k. Heuristics for computing the contraction degeneracy are proposed and evaluated. It is shown that these can lead in practice to considerable improvements of the lower bound for treewidth, but can perform arbitrarily bad on some examples. A study is also made for the combination of contraction with Lucena's lower bound based on Maximum Cardinality Search [23]. Finally, heuristics for the treewidth are proposed and evaluated that combine contraction with a treewidth lower bound technique by Clautiaux et al. [12]." | |
| 650 | 4 | |a Decomposition (Mathematics) | |
| 650 | 4 | |a Trees (Graph theory) | |
| 700 | 1 | |a Koster, Arie M. C. A. |e Verfasser |4 aut | |
| 700 | 1 | |a Wolle, Thomas |e Verfasser |4 aut | |
| 830 | 0 | |a ZIB-Report |v 2004,29 |w (DE-604)BV013191727 |9 2004,29 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-012871515 | |
Datensatz im Suchindex
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| author | Bodlaender, Hans L. Koster, Arie M. C. A. Wolle, Thomas |
| author_facet | Bodlaender, Hans L. Koster, Arie M. C. A. Wolle, Thomas |
| author_role | aut aut aut |
| author_sort | Bodlaender, Hans L. |
| author_variant | h l b hl hlb a m c a k amca amcak t w tw |
| building | Verbundindex |
| bvnumber | BV019409502 |
| classification_rvk | SS 4779 |
| ctrlnum | (OCoLC)57072787 (DE-599)BVBBV019409502 |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV019409502 |
| illustrated | Illustrated |
| indexdate | 2025-01-10T17:06:53Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012871515 |
| oclc_num | 57072787 |
| open_access_boolean | |
| owner | DE-703 DE-188 |
| owner_facet | DE-703 DE-188 |
| physical | 33 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik |
| record_format | marc |
| series | ZIB-Report |
| series2 | ZIB-Report |
| spelling | Bodlaender, Hans L. Verfasser aut Contraction and treewidth lower bounds Hans L. Bodlaender ; Arie M. C. A. Koster ; Thomas Wolle Berlin Konrad-Zuse-Zentrum für Informationstechnik 2004 33 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier ZIB-Report 2004,29 Abstract: "Edge contraction is shown to be a useful mechanism to improve lower bound heuristics for treewidth. A successful lower bound for treewidth is the degeneracy: the maximum over all subgraphs of the minimum degree. The degeneracy is polynomial time computable. We introduce the notion of contraction degeneracy: the maximum over all minors of the minimum degree. We show that the contraction degeneracy problem is NP-complete, even for bipartite graphs, but for fixed k, it is polynomial time decidable if a given graph G has contraction degeneracy at least k. Heuristics for computing the contraction degeneracy are proposed and evaluated. It is shown that these can lead in practice to considerable improvements of the lower bound for treewidth, but can perform arbitrarily bad on some examples. A study is also made for the combination of contraction with Lucena's lower bound based on Maximum Cardinality Search [23]. Finally, heuristics for the treewidth are proposed and evaluated that combine contraction with a treewidth lower bound technique by Clautiaux et al. [12]." Decomposition (Mathematics) Trees (Graph theory) Koster, Arie M. C. A. Verfasser aut Wolle, Thomas Verfasser aut ZIB-Report 2004,29 (DE-604)BV013191727 2004,29 |
| spellingShingle | Bodlaender, Hans L. Koster, Arie M. C. A. Wolle, Thomas Contraction and treewidth lower bounds ZIB-Report Decomposition (Mathematics) Trees (Graph theory) |
| title | Contraction and treewidth lower bounds |
| title_auth | Contraction and treewidth lower bounds |
| title_exact_search | Contraction and treewidth lower bounds |
| title_full | Contraction and treewidth lower bounds Hans L. Bodlaender ; Arie M. C. A. Koster ; Thomas Wolle |
| title_fullStr | Contraction and treewidth lower bounds Hans L. Bodlaender ; Arie M. C. A. Koster ; Thomas Wolle |
| title_full_unstemmed | Contraction and treewidth lower bounds Hans L. Bodlaender ; Arie M. C. A. Koster ; Thomas Wolle |
| title_short | Contraction and treewidth lower bounds |
| title_sort | contraction and treewidth lower bounds |
| topic | Decomposition (Mathematics) Trees (Graph theory) |
| topic_facet | Decomposition (Mathematics) Trees (Graph theory) |
| volume_link | (DE-604)BV013191727 |
| work_keys_str_mv | AT bodlaenderhansl contractionandtreewidthlowerbounds AT kosterariemca contractionandtreewidthlowerbounds AT wollethomas contractionandtreewidthlowerbounds |