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

Shuji Kijima, Masashi Kiyomi, Yoshio Okamoto, Takeaki Uno

Research output: Contribution to journalArticle

1 Citation (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 that at least one of the input graphs 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 indicate 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
Pages (from-to)2591-2601
Number of pages11
JournalTheoretical Computer Science
Volume411
Issue number26-28
DOIs
Publication statusPublished - Jun 6 2010

Fingerprint

Chordal Graphs
Counting
Polynomials
Sampling
Markov processes
Data mining
Statistics
Counting Problems
Mixing Time
Random Sampling
Graph in graph theory
Numerical Computation
Deletion
Completion
Completeness
Markov chain
Data Mining
Polynomial time
Count
Efficient Algorithms

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

On listing, sampling, and counting the chordal graphs with edge constraints. / Kijima, Shuji; Kiyomi, Masashi; Okamoto, Yoshio; Uno, Takeaki.

In: Theoretical Computer Science, Vol. 411, No. 26-28, 06.06.2010, p. 2591-2601.

Research output: Contribution to journalArticle

Kijima, Shuji ; Kiyomi, Masashi ; Okamoto, Yoshio ; Uno, Takeaki. / On listing, sampling, and counting the chordal graphs with edge constraints. In: Theoretical Computer Science. 2010 ; Vol. 411, No. 26-28. pp. 2591-2601.
@article{e3a7183aa6824531913dc7965996d7fc,
title = "On listing, sampling, and counting the chordal graphs with edge constraints",
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 that at least one of the input graphs 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 indicate 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.",
author = "Shuji Kijima and Masashi Kiyomi and Yoshio Okamoto and Takeaki Uno",
year = "2010",
month = "6",
day = "6",
doi = "10.1016/j.tcs.2010.03.024",
language = "English",
volume = "411",
pages = "2591--2601",
journal = "Theoretical Computer Science",
issn = "0304-3975",
publisher = "Elsevier",
number = "26-28",

}

TY - JOUR

T1 - On listing, sampling, and counting the chordal graphs with edge constraints

AU - Kijima, Shuji

AU - Kiyomi, Masashi

AU - Okamoto, Yoshio

AU - Uno, Takeaki

PY - 2010/6/6

Y1 - 2010/6/6

N2 - 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 that at least one of the input graphs 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 indicate 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.

AB - 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 that at least one of the input graphs 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 indicate 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.

UR - http://www.scopus.com/inward/record.url?scp=77953288766&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953288766&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2010.03.024

DO - 10.1016/j.tcs.2010.03.024

M3 - Article

AN - SCOPUS:77953288766

VL - 411

SP - 2591

EP - 2601

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 26-28

ER -