Treewidth: computational experiments
Abstract: "Many NP-hard graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
2001
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| Schriftenreihe: | ZIB-Report
2001,38 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "Many NP-hard graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to find (almost) optimal solutions or lower bounds for many optimization problems. To apply a tree decomposition approach, the treewidth of the graph has to be determined, independently of the application at hand. Althouh for fixed k, linear time algorithms exist to solve the decision problem 'treewidth [<or =] k', their practical use is very limited. The computational tractability of treewidth has been rarely studied so far. In this paper, we compare four heuristics and two lower bounds for instances from applications such as the frequency assignment problem and the vertex coloring problem. Three of the heuristics are based on well-known algorithms to recognize triangulated graphs. The fourth heuristic recursively improves a tree decomposition by the computation of minimal separating vertex sets in subgraphs. Lower bounds can be computed from maximal cliques and the minimum degree of induced subgraphs. A computational analysis shows that the treewidth of several graphs can be identified by these methods. For other graphs, however, more sophisticated techniques are necessary." |
| Beschreibung: | 24 S. Ill., graph. Darst. |
Internformat
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| 100 | 1 | |a Koster, Arie M. C. A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Treewidth |b computational experiments |c Arie M. C. A. Koster ; Hans L. Bodlaender ; Stan P. M. van Hoesel |
| 264 | 1 | |a Berlin |b Konrad-Zuse-Zentrum für Informationstechnik |c 2001 | |
| 300 | |a 24 S. |b Ill., graph. Darst. | ||
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| 490 | 1 | |a ZIB-Report |v 2001,38 | |
| 520 | 3 | |a Abstract: "Many NP-hard graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to find (almost) optimal solutions or lower bounds for many optimization problems. To apply a tree decomposition approach, the treewidth of the graph has to be determined, independently of the application at hand. Althouh for fixed k, linear time algorithms exist to solve the decision problem 'treewidth [<or =] k', their practical use is very limited. The computational tractability of treewidth has been rarely studied so far. In this paper, we compare four heuristics and two lower bounds for instances from applications such as the frequency assignment problem and the vertex coloring problem. Three of the heuristics are based on well-known algorithms to recognize triangulated graphs. The fourth heuristic recursively improves a tree decomposition by the computation of minimal separating vertex sets in subgraphs. Lower bounds can be computed from maximal cliques and the minimum degree of induced subgraphs. A computational analysis shows that the treewidth of several graphs can be identified by these methods. For other graphs, however, more sophisticated techniques are necessary." | |
| 650 | 4 | |a Decomposition (Mathematics) | |
| 650 | 4 | |a Heuristic programming | |
| 650 | 4 | |a Trees (Graph theory) | |
| 700 | 1 | |a Bodlaender, Hans L. |e Verfasser |4 aut | |
| 700 | 1 | |a Hoesel, Stan P. M. van |e Verfasser |4 aut | |
| 830 | 0 | |a ZIB-Report |v 2001,38 |w (DE-604)BV013191727 |9 2001,38 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016238535 | ||
Datensatz im Suchindex
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| author | Koster, Arie M. C. A. Bodlaender, Hans L. Hoesel, Stan P. M. van |
| author_facet | Koster, Arie M. C. A. Bodlaender, Hans L. Hoesel, Stan P. M. van |
| author_role | aut aut aut |
| author_sort | Koster, Arie M. C. A. |
| author_variant | a m c a k amca amcak h l b hl hlb s p m v h spmv spmvh |
| building | Verbundindex |
| bvnumber | BV023034736 |
| classification_rvk | SS 4779 |
| ctrlnum | (OCoLC)50181465 (DE-599)BVBBV023034736 |
| discipline | Informatik |
| discipline_str_mv | Informatik |
| format | Book |
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| id | DE-604.BV023034736 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:18:25Z |
| indexdate | 2024-07-09T21:09:29Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016238535 |
| oclc_num | 50181465 |
| open_access_boolean | |
| owner | DE-703 DE-188 |
| owner_facet | DE-703 DE-188 |
| physical | 24 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik |
| record_format | marc |
| series | ZIB-Report |
| series2 | ZIB-Report |
| spelling | Koster, Arie M. C. A. Verfasser aut Treewidth computational experiments Arie M. C. A. Koster ; Hans L. Bodlaender ; Stan P. M. van Hoesel Berlin Konrad-Zuse-Zentrum für Informationstechnik 2001 24 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier ZIB-Report 2001,38 Abstract: "Many NP-hard graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to find (almost) optimal solutions or lower bounds for many optimization problems. To apply a tree decomposition approach, the treewidth of the graph has to be determined, independently of the application at hand. Althouh for fixed k, linear time algorithms exist to solve the decision problem 'treewidth [<or =] k', their practical use is very limited. The computational tractability of treewidth has been rarely studied so far. In this paper, we compare four heuristics and two lower bounds for instances from applications such as the frequency assignment problem and the vertex coloring problem. Three of the heuristics are based on well-known algorithms to recognize triangulated graphs. The fourth heuristic recursively improves a tree decomposition by the computation of minimal separating vertex sets in subgraphs. Lower bounds can be computed from maximal cliques and the minimum degree of induced subgraphs. A computational analysis shows that the treewidth of several graphs can be identified by these methods. For other graphs, however, more sophisticated techniques are necessary." Decomposition (Mathematics) Heuristic programming Trees (Graph theory) Bodlaender, Hans L. Verfasser aut Hoesel, Stan P. M. van Verfasser aut ZIB-Report 2001,38 (DE-604)BV013191727 2001,38 |
| spellingShingle | Koster, Arie M. C. A. Bodlaender, Hans L. Hoesel, Stan P. M. van Treewidth computational experiments ZIB-Report Decomposition (Mathematics) Heuristic programming Trees (Graph theory) |
| title | Treewidth computational experiments |
| title_auth | Treewidth computational experiments |
| title_exact_search | Treewidth computational experiments |
| title_exact_search_txtP | Treewidth computational experiments |
| title_full | Treewidth computational experiments Arie M. C. A. Koster ; Hans L. Bodlaender ; Stan P. M. van Hoesel |
| title_fullStr | Treewidth computational experiments Arie M. C. A. Koster ; Hans L. Bodlaender ; Stan P. M. van Hoesel |
| title_full_unstemmed | Treewidth computational experiments Arie M. C. A. Koster ; Hans L. Bodlaender ; Stan P. M. van Hoesel |
| title_short | Treewidth |
| title_sort | treewidth computational experiments |
| title_sub | computational experiments |
| topic | Decomposition (Mathematics) Heuristic programming Trees (Graph theory) |
| topic_facet | Decomposition (Mathematics) Heuristic programming Trees (Graph theory) |
| volume_link | (DE-604)BV013191727 |
| work_keys_str_mv | AT kosterariemca treewidthcomputationalexperiments AT bodlaenderhansl treewidthcomputationalexperiments AT hoeselstanpmvan treewidthcomputationalexperiments |