Weak-order extensions of an order
Identifieur interne : 003957 ( Crin/Curation ); précédent : 003956; suivant : 003958Weak-order extensions of an order
Auteurs : Karell Bertet ; Jens Gustedt ; Michel MorvanSource :
- Theoretical Computer Science ; 2003.
English descriptors
- KwdEn :
Abstract
In this paper, at first we describe a digraph representing all the weak-order extensions of a partially ordered set and algorithms for generating them. Then we present a digraph representing all of the minimal weak-order extensions of a partially ordered set. This digraph also implies generation algorithms. Finally, we prove that the number of weak-order extensions of a partially ordered set is a comparability invariant, whereas the number of minimal weak-order extensions of a partially ordered set is not a comparability invariant.
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<author><name sortKey="Gustedt, Jens" sort="Gustedt, Jens" uniqKey="Gustedt J" first="Jens" last="Gustedt">Jens Gustedt</name>
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<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>algorithm</term>
<term>complexity</term>
<term>extension of an order</term>
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<term>weak-order</term>
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<front><div type="abstract" xml:lang="en" wicri:score="1359">In this paper, at first we describe a digraph representing all the weak-order extensions of a partially ordered set and algorithms for generating them. Then we present a digraph representing all of the minimal weak-order extensions of a partially ordered set. This digraph also implies generation algorithms. Finally, we prove that the number of weak-order extensions of a partially ordered set is a comparability invariant, whereas the number of minimal weak-order extensions of a partially ordered set is not a comparability invariant.</div>
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<BibTex type="article"><ref>bertet03a</ref>
<crinnumber>A03-R-225</crinnumber>
<category>1</category>
<equipe>L3I</equipe>
<author><e>Bertet, Karell</e>
<e>Gustedt, Jens</e>
<e>Morvan, Michel</e>
</author>
<title>Weak-order extensions of an order</title>
<journal>Theoretical Computer Science</journal>
<year>2003</year>
<volume>304</volume>
<number>1-3</number>
<pages>249-268</pages>
<month>Jul</month>
<keywords><e>partial order</e>
<e>algorithm</e>
<e>weak-order</e>
<e>extension of an order</e>
<e>graph</e>
<e>complexity</e>
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<abstract>In this paper, at first we describe a digraph representing all the weak-order extensions of a partially ordered set and algorithms for generating them. Then we present a digraph representing all of the minimal weak-order extensions of a partially ordered set. This digraph also implies generation algorithms. Finally, we prove that the number of weak-order extensions of a partially ordered set is a comparability invariant, whereas the number of minimal weak-order extensions of a partially ordered set is not a comparability invariant.</abstract>
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