On the maximum cardinality search lower bound for treewidth:
Abstract: "The Maximum Cardinality Search algorithm visits the vertices of a graph in some order, such that at each step, an unvisited vertex that has the largest number of visited neighbors becomes visited. An MCS-ordering of a graph is an ordering of the vertices that can be generated by the...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
2004
|
| Schriftenreihe: | ZIB
2004,45 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "The Maximum Cardinality Search algorithm visits the vertices of a graph in some order, such that at each step, an unvisited vertex that has the largest number of visited neighbors becomes visited. An MCS-ordering of a graph is an ordering of the vertices that can be generated by the Maximum Cardinality Search algorithm. The visited degree of a vertex v in an MCS-ordering is the number of neighbors of v that are before v in the ordering. The visited degree of an MCS-ordering [psi] of G is the maximum visited degree over all vertices v in [psi]. The maximum visited degree over all MCS-orderings of graph G is called its maximum visited degree. Lucena [14] showed that the treewidth of a graph G is at least its maximum visited degree. We show that the maximum visited degree is of size O(log n) for planar graphs, and give examples of planar graphs G with maximum visited degree k with O(k!) vertices, for all k [element of] N. Given a graph G, it is NP-complete to determine if its maximum visited degree is at least k, for any fixed k [> or =] 7. Also, this problem does not have a polynomial time approximation algorithm with constant ratio, unless P = NP. Variants of the problem are also shown to be NP-complete. We also propose and experimentally analysed some heuristics for the problem. Several tiebreakers for the MCS algorithm are proposed and evaluated. We also give heuristics that give upper bounds on the value of the maximum visited degree of a graph, which appear to give results close to optimal on many graphs from real life applications." |
| Beschreibung: | 32 S. graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Bodlaender, Hans L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a On the maximum cardinality search lower bound for treewidth |c Hans L. Bodlaender ; Arie M. C. A. Koster |
| 264 | 1 | |a Berlin |b Konrad-Zuse-Zentrum für Informationstechnik |c 2004 | |
| 300 | |a 32 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a ZIB |v 2004,45 | |
| 520 | 3 | |a Abstract: "The Maximum Cardinality Search algorithm visits the vertices of a graph in some order, such that at each step, an unvisited vertex that has the largest number of visited neighbors becomes visited. An MCS-ordering of a graph is an ordering of the vertices that can be generated by the Maximum Cardinality Search algorithm. The visited degree of a vertex v in an MCS-ordering is the number of neighbors of v that are before v in the ordering. The visited degree of an MCS-ordering [psi] of G is the maximum visited degree over all vertices v in [psi]. The maximum visited degree over all MCS-orderings of graph G is called its maximum visited degree. Lucena [14] showed that the treewidth of a graph G is at least its maximum visited degree. We show that the maximum visited degree is of size O(log n) for planar graphs, and give examples of planar graphs G with maximum visited degree k with O(k!) vertices, for all k [element of] N. Given a graph G, it is NP-complete to determine if its maximum visited degree is at least k, for any fixed k [> or =] 7. Also, this problem does not have a polynomial time approximation algorithm with constant ratio, unless P = NP. Variants of the problem are also shown to be NP-complete. We also propose and experimentally analysed some heuristics for the problem. Several tiebreakers for the MCS algorithm are proposed and evaluated. We also give heuristics that give upper bounds on the value of the maximum visited degree of a graph, which appear to give results close to optimal on many graphs from real life applications." | |
| 650 | 4 | |a Computer algorithms | |
| 650 | 4 | |a Trees (Graph theory) | |
| 700 | 1 | |a Koster, Arie M. C. A. |e Verfasser |4 aut | |
| 830 | 0 | |a ZIB |v 2004,45 |w (DE-604)BV013191727 |9 2004,45 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-012971980 | ||
Datensatz im Suchindex
| _version_ | 1804133015736025088 |
|---|---|
| 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 | BV019643148 |
| classification_rvk | SS 4779 |
| ctrlnum | (OCoLC)60248898 (DE-599)BVBBV019643148 |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV019643148 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:02:00Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012971980 |
| oclc_num | 60248898 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | 32 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik |
| record_format | marc |
| series | ZIB |
| series2 | ZIB |
| spelling | Bodlaender, Hans L. Verfasser aut On the maximum cardinality search lower bound for treewidth Hans L. Bodlaender ; Arie M. C. A. Koster Berlin Konrad-Zuse-Zentrum für Informationstechnik 2004 32 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier ZIB 2004,45 Abstract: "The Maximum Cardinality Search algorithm visits the vertices of a graph in some order, such that at each step, an unvisited vertex that has the largest number of visited neighbors becomes visited. An MCS-ordering of a graph is an ordering of the vertices that can be generated by the Maximum Cardinality Search algorithm. The visited degree of a vertex v in an MCS-ordering is the number of neighbors of v that are before v in the ordering. The visited degree of an MCS-ordering [psi] of G is the maximum visited degree over all vertices v in [psi]. The maximum visited degree over all MCS-orderings of graph G is called its maximum visited degree. Lucena [14] showed that the treewidth of a graph G is at least its maximum visited degree. We show that the maximum visited degree is of size O(log n) for planar graphs, and give examples of planar graphs G with maximum visited degree k with O(k!) vertices, for all k [element of] N. Given a graph G, it is NP-complete to determine if its maximum visited degree is at least k, for any fixed k [> or =] 7. Also, this problem does not have a polynomial time approximation algorithm with constant ratio, unless P = NP. Variants of the problem are also shown to be NP-complete. We also propose and experimentally analysed some heuristics for the problem. Several tiebreakers for the MCS algorithm are proposed and evaluated. We also give heuristics that give upper bounds on the value of the maximum visited degree of a graph, which appear to give results close to optimal on many graphs from real life applications." Computer algorithms Trees (Graph theory) Koster, Arie M. C. A. Verfasser aut ZIB 2004,45 (DE-604)BV013191727 2004,45 |
| spellingShingle | Bodlaender, Hans L. Koster, Arie M. C. A. On the maximum cardinality search lower bound for treewidth ZIB Computer algorithms Trees (Graph theory) |
| title | On the maximum cardinality search lower bound for treewidth |
| title_auth | On the maximum cardinality search lower bound for treewidth |
| title_exact_search | On the maximum cardinality search lower bound for treewidth |
| title_full | On the maximum cardinality search lower bound for treewidth Hans L. Bodlaender ; Arie M. C. A. Koster |
| title_fullStr | On the maximum cardinality search lower bound for treewidth Hans L. Bodlaender ; Arie M. C. A. Koster |
| title_full_unstemmed | On the maximum cardinality search lower bound for treewidth Hans L. Bodlaender ; Arie M. C. A. Koster |
| title_short | On the maximum cardinality search lower bound for treewidth |
| title_sort | on the maximum cardinality search lower bound for treewidth |
| topic | Computer algorithms Trees (Graph theory) |
| topic_facet | Computer algorithms Trees (Graph theory) |
| volume_link | (DE-604)BV013191727 |
| work_keys_str_mv | AT bodlaenderhansl onthemaximumcardinalitysearchlowerboundfortreewidth AT kosterariemca onthemaximumcardinalitysearchlowerboundfortreewidth |