Computing the Clique-Width of Large Path Powers in Linear Time via a New Characterisation of Clique-Width
Identifieur interne : 000010 ( LNCS/Analysis ); précédent : 000009; suivant : 000011Computing the Clique-Width of Large Path Powers in Linear Time via a New Characterisation of Clique-Width
Auteurs : Pinar Heggernes [Norvège] ; Daniel Meister [Allemagne] ; Udi Rotics [Israël]Source :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2011.
Abstract
Abstract: Clique-width is one of the most important graph parameters, as many NP-hard graph problems are solvable in linear time on graphs of bounded clique-width. Unfortunately, the computation of clique-width is among the hardest problems. In fact, we do not know of any other algorithm than brute force for the exact computation of clique-width on any large graph class of unbounded clique-width. Another difficulty about clique-width is the lack of alternative characterisations of it that might help in coping with its hardness. In this paper, we present two results. The first is a new characterisation of clique-width based on rooted binary trees, completely without the use of labelled graphs. Our second result is the exact computation of the clique-width of large path powers in polynomial time, which has been an open problem for a decade. The presented new characterisation is used to achieve this latter result. With our result, large k-path powers constitute the first non-trivial infinite class of graphs of unbounded clique-width whose clique-width can be computed exactly in polynomial time.
Url:
DOI: 10.1007/978-3-642-20712-9_18
Affiliations:
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Unfortunately, the computation of clique-width is among the hardest problems. In fact, we do not know of any other algorithm than brute force for the exact computation of clique-width on any large graph class of unbounded clique-width. Another difficulty about clique-width is the lack of alternative characterisations of it that might help in coping with its hardness. In this paper, we present two results. The first is a new characterisation of clique-width based on rooted binary trees, completely without the use of labelled graphs. Our second result is the exact computation of the clique-width of large path powers in polynomial time, which has been an open problem for a decade. The presented new characterisation is used to achieve this latter result. With our result, large k-path powers constitute the first non-trivial infinite class of graphs of unbounded clique-width whose clique-width can be computed exactly in polynomial time.</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>Israël</li><li>Norvège</li></country><region><li>Rhénanie-Palatinat</li></region><settlement><li>Trèves (Allemagne)</li></settlement><orgName><li>Université de Trèves</li></orgName></list><tree><country name="Norvège"><noRegion><name sortKey="Heggernes, Pinar" sort="Heggernes, Pinar" uniqKey="Heggernes P" first="Pinar" last="Heggernes">Pinar Heggernes</name></noRegion><name sortKey="Heggernes, Pinar" sort="Heggernes, Pinar" uniqKey="Heggernes P" first="Pinar" last="Heggernes">Pinar Heggernes</name></country><country name="Allemagne"><region name="Rhénanie-Palatinat"><name sortKey="Meister, Daniel" sort="Meister, Daniel" uniqKey="Meister D" first="Daniel" last="Meister">Daniel Meister</name></region><name sortKey="Meister, Daniel" sort="Meister, Daniel" uniqKey="Meister D" first="Daniel" last="Meister">Daniel Meister</name></country><country name="Israël"><noRegion><name sortKey="Rotics, Udi" sort="Rotics, Udi" uniqKey="Rotics U" first="Udi" last="Rotics">Udi Rotics</name></noRegion><name sortKey="Rotics, Udi" sort="Rotics, Udi" uniqKey="Rotics U" first="Udi" last="Rotics">Udi Rotics</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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