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On Listing, Sampling, and Counting the Chordal Graphs with Edge Constraints

  • Shuji Kijima
  • Masashi Kiyomi
  • Yoshio Okamoto
  • Takeaki Uno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)

Abstract

We discuss the problems to list, sample, and count the chordal graphs with edge constraints. The objects we look at are chordal graphs sandwiched by a given pair of graphs where we assume at least one of the input pair is chordal. The setting is a natural generalization of chordal completions and deletions. For the listing problem, we give an efficient algorithm running in polynomial time per output with polynomial space. As for the sampling problem, we give two clues that seem to imply that a random sampling is not easy. The first clue is that we show #P-completeness results for counting problems. The second clue is that we give an instance for which a natural Markov chain suffers from an exponential mixing time. These results provide a unified viewpoint from algorithms theory to problems arising from various areas such as statistics, data mining, and numerical computation.

Keywords

Markov Chain SIAM Journal Interval Graph Chordal Graph Listing Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Shuji Kijima
    • 1
  • Masashi Kiyomi
    • 2
  • Yoshio Okamoto
    • 3
  • Takeaki Uno
    • 4
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  2. 2.School of Information ScienceJapan Advanced Institute of Science and TechnologyNomiJapan
  3. 3.Graduate School of Information Science and EngineeringTokyo Institute of TechnologyTokyoJapan
  4. 4.National Institute of InformaticsTokyoJapan

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