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Creators/Authors contains: "Hébert-Johnson, Úrsula"

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  1. ; ; (, 31st Annual European Symposium on Algorithms (ESA))
    Accepted Manuscript Full Text Available
  2. ; ; (, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)
    Gørtz, Inge Li; Farach-Colton, Martin; Puglisi, Simon J; Herman, Grzegorz (Ed.)
    We present the first polynomial-time algorithm to exactly compute the number of labeled chordal graphs on n vertices. Our algorithm solves a more general problem: given n and ω as input, it computes the number of ω-colorable labeled chordal graphs on n vertices, using O(n⁷) arithmetic operations. A standard sampling-to-counting reduction then yields a polynomial-time exact sampler that generates an ω-colorable labeled chordal graph on n vertices uniformly at random. Our counting algorithm improves upon the previous best result by Wormald (1985), which computes the number of labeled chordal graphs on n vertices in time exponential in n. An implementation of the polynomial-time counting algorithm gives the number of labeled chordal graphs on up to 30 vertices in less than three minutes on a standard desktop computer. Previously, the number of labeled chordal graphs was only known for graphs on up to 15 vertices. 
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  3. ; ; ; (, Procedia Computer Science)
    Full Text Available