On listing, sampling, and counting the chordal graphs with edge constraints

Shuji Kijima, Masashi Kiyomi, Yoshio Okamoto, Takeaki Uno

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 14th Annual International Conference, COCOON 2008, Proceedings
Pages458-467
Number of pages10
DOIs
Publication statusPublished - Aug 4 2008
Externally publishedYes
Event14th Annual International Conference on Computing and Combinatorics, COCOON 2008 - Dalian, China
Duration: Jun 27 2008Jun 29 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5092 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other14th Annual International Conference on Computing and Combinatorics, COCOON 2008
CountryChina
CityDalian
Period6/27/086/29/08

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Kijima, S., Kiyomi, M., Okamoto, Y., & Uno, T. (2008). On listing, sampling, and counting the chordal graphs with edge constraints. In Computing and Combinatorics - 14th Annual International Conference, COCOON 2008, Proceedings (pp. 458-467). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5092 LNCS). https://doi.org/10.1007/978-3-540-69733-6_45