Computing the Clique-Width of Large Path Powers in Linear Time via a New Characterisation of Clique-Width
Identifieur interne : 001A17 ( Istex/Curation ); précédent : 001A16; suivant : 001A18Computing 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.
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DOI: 10.1007/978-3-642-20712-9_18
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xml:lang="en">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.</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
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