Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
Journal of Algorithms
Reverse search for enumeration
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
A Polynomial Approximation Algorithm for the Minimum Fill-In Problem
SIAM Journal on Computing
Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework
SIAM Journal on Optimization
Computing Treewidth and Minimum Fill-In: All You Need are the Minimal Separators
ESA '93 Proceedings of the First Annual European Symposium on Algorithms
Sequential model selection for word sense disambiguation
ANLC '97 Proceedings of the fifth conference on Applied natural language processing
Generating Chordal Graphs Included in Given Graphs
IEICE - Transactions on Information and Systems
Fully dynamic algorithms for chordal graphs and split graphs
ACM Transactions on Algorithms (TALG)
Sparse quasi-Newton updates with positive definite matrix completion
Mathematical Programming: Series A and B
Exact Algorithms for Treewidth and Minimum Fill-In
SIAM Journal on Computing
Graphical Models in Applied Multivariate Statistics
Graphical Models in Applied Multivariate Statistics
Characterizing minimal interval completions towards better understanding of profile and pathwidth
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
Listing chordal graphs and interval graphs
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Efficient enumeration of the directed binary perfect phylogenies from incomplete data
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
Hi-index | 5.23 |
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.