On the complexity of cycle enumeration using Zeons
Identifieur interne : 003235 ( Main/Exploration ); précédent : 003234; suivant : 003236On the complexity of cycle enumeration using Zeons
Auteurs : René Schott [France] ; Stacey Staples [États-Unis]Source :
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Abstract
Nilpotent adjacency matrix methods are employed to enumerate $k$-cycles in simple graphs on $n$ vertices for any $k\le n$. The worst-case time complexity of counting $k$-cycles in an $n$-vertex simple graph is shown to be $\mathcal{O}(n^{\alpha+1} 2^{n})$, where $\alpha\le 3$ is the exponent representing the complexity of matrix multiplication. When $k$ is fixed, the enumeration of all $k$-cycles in an $n$-vertex graph is of time complexity $\mathcal{O}(n^{\alpha+k-1})$. Letting $\Omega=\binom{n}{2}$, the average-case time complexity of counting $k$-cycles in an $n$-vertex, $e$-edge graph where $e\le \displaystyle q\left(\frac{\Omega}{k}-1\right)$ for fixed $0
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Affiliations:
- France, États-Unis
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
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Le document en format XML
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The worst-case time complexity of counting $k$-cycles in an $n$-vertex simple graph is shown to be $\mathcal{O}(n^{\alpha+1} 2^{n})$, where $\alpha\le 3$ is the exponent representing the complexity of matrix multiplication. When $k$ is fixed, the enumeration of all $k$-cycles in an $n$-vertex graph is of time complexity $\mathcal{O}(n^{\alpha+k-1})$. Letting $\Omega=\binom{n}{2}$, the average-case time complexity of counting $k$-cycles in an $n$-vertex, $e$-edge graph where $e\le \displaystyle q\left(\frac{\Omega}{k}-1\right)$ for fixed $0</div> </front></TEI><affiliations><list><country><li>France</li><li>États-Unis</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Nancy</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Nancy 2</li><li>Université de Lorraine</li></orgName></list><tree><country name="France"><region name="Grand Est"><name sortKey="Schott, Rene" sort="Schott, Rene" uniqKey="Schott R" first="René" last="Schott">René Schott</name></region></country><country name="États-Unis"><noRegion><name sortKey="Staples, Stacey" sort="Staples, Stacey" uniqKey="Staples S" first="Stacey" last="Staples">Stacey Staples</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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