On the complexity of computing treelength
We resolve the computational complexity of determining the treelength of a graph, thereby solving an open problem of Dourisboure and Gavoille, who introduced this parameter, and asked to determine the complexity of recognizing graphs of a bounded treelength Dourisboure and Gavoille (2007) [6]. Whil...
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| Veröffentlicht in: | Discrete Applied Mathematics Jg. 158; H. 7; S. 820 - 827 |
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| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Elsevier B.V
06.04.2010
|
| Schlagworte: | |
| ISSN: | 0166-218X, 1872-6771 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We resolve the computational complexity of determining the
treelength of a graph, thereby solving an open problem of Dourisboure and Gavoille, who introduced this parameter, and asked to determine the complexity of recognizing graphs of a bounded treelength Dourisboure and Gavoille (2007)
[6]. While recognizing graphs with treelength 1 is easily seen as equivalent to recognizing chordal graphs, which can be done in linear time, the computational complexity of recognizing graphs with treelength 2 was unknown until this result. We show that the problem of determining whether a given graph has a treelength at most
k
is NP-complete for every fixed
k
≥
2
, and use this result to show that treelength in weighted graphs is hard to approximate within a factor smaller than
3
2
. Additionally, we show that treelength can be computed in time
O
∗
(
1.754
9
n
)
by giving an exact exponential time algorithm for the Chordal Sandwich problem and showing how this algorithm can be used to compute the treelength of a graph. |
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| ISSN: | 0166-218X 1872-6771 |
| DOI: | 10.1016/j.dam.2009.10.007 |