Introduction to algorithms
A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Counting the number of solutions for instances of satisfiability
Theoretical Computer Science
The design and analysis of algorithms
The design and analysis of algorithms
Number of models and satisfiability of sets of clauses
Theoretical Computer Science
Linear Algorithms for Partitioning Embedded Graphs of BoundedGenus
SIAM Journal on Discrete Mathematics
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
New methods for 3-SAT decision and worst-case analysis
Theoretical Computer Science
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
An algorithm for counting maximum weighted independent sets and its applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Counting H-colorings of partial k-trees
Theoretical Computer Science
The Complexity of Counting in Sparse, Regular, and Planar Graphs
SIAM Journal on Computing
Counting Satisfying Assignments in 2-SAT and 3-SAT
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Counting Models Using Connected Components
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
New upper bound for the #3-SAT problem
Information Processing Letters
Exact Max 2-Sat: Easier and Faster
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Algorithms for Counting 2-Sat Solutions and Colorings with Applications
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Polynomial constraint satisfaction problems, graph bisection, and the Ising partition function
ACM Transactions on Algorithms (TALG)
The union of minimal hitting sets: Parameterized combinatorial bounds and counting
Journal of Discrete Algorithms
A worst-case time upper bound for counting the number of independent sets
CAAN'07 Proceedings of the 4th conference on Combinatorial and algorithmic aspects of networking
A tighter bound for counting max-weight solutions to 2SAT instances
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Solving NP-complete problems with quantum search
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
An algorithm for the SAT problem for formulae of linear length
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Faster exact solving of SAT formulae with a low number of occurrences per variable
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Partitioning based algorithms for some colouring problems
CSCLP'05 Proceedings of the 2005 Joint ERCIM/CoLogNET international conference on Constraint Solving and Constraint Logic Programming
Branching and treewidth based exact algorithms
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
A faster algorithm for finding maximum independent sets in sparse graphs
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Counting independent sets in claw-free graphs
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Counting maximal independent sets in subcubic graphs
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Linear-programming design and analysis of fast algorithms for Max 2-CSP
Discrete Optimization
Estimating entity importance via counting set covers
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Computing #2SAT and #2UNSAT by binary patterns
MCPR'12 Proceedings of the 4th Mexican conference on Pattern Recognition
Counting minimum weighted dominating sets
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
| Hi-index | 5.23 |
We here present algorithms for counting models and max-weight models for 2SAT and 3SAT formulae. They use polynomial space and run in O(1.2561n) and O(1.6737n) time, respectively, where n is the number of variables. This is faster than the previously best algorithms for counting nonweighted models for 2SAT and 3SAT, which run in O(1.3247n) and O(1.6894n) time, respectively. In order to prove these time bounds, we develop new measures of formula complexity, allowing us to conveniently analyze the effects of certain factors with a large impact on the total running time. We also provide an algorithm for the restricted case of separable 2SAT formulae, with fast running times for well-studied input classes. For all three algorithms we present interesting applications, such as computing the permanent of sparse 0/1 matrices.