Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
Journal of Algorithms
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Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
Fully dynamic algorithms for chordal graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
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SIAM Journal on Computing
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ESA '93 Proceedings of the First Annual European Symposium on Algorithms
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ANLC '97 Proceedings of the fifth conference on Applied natural language processing
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
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IEICE - Transactions on Information and Systems
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STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Chordal deletion is fixed-parameter tractable
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
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WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Strongly Chordal and Chordal Bipartite Graphs Are Sandwich Monotone
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Strongly chordal and chordal bipartite graphs are sandwich monotone
Journal of Combinatorial Optimization
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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.