Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications
ACM Transactions on Algorithms (TALG)
Counting Subgraphs via Homomorphisms
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Polynomial constraint satisfaction problems, graph bisection, and the Ising partition function
ACM Transactions on Algorithms (TALG)
Exact structure discovery in Bayesian networks with less space
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
A space-time tradeoff for permutation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Exponential time complexity of the permanent and the Tutte polynomial
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Preprocessing of min ones problems: a dichotomy
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Exact and parameterized algorithms for edge dominating set in 3-degree graphs
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Invitation to algorithmic uses of inclusion-exclusion
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Counting perfect matchings as fast as Ryser
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Solving single-digit sudoku subproblems
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
Counting perfect matchings in graphs of degree 3
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
The hardness of counting full words compatible with partial words
Journal of Computer and System Sciences
Finding optimal Bayesian networks using precedence constraints
The Journal of Machine Learning Research
Exponential approximation schemata for some network design problems
Journal of Discrete Algorithms
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We present exact algorithms with exponential running times for variants of n-element set cover problems, based on divide-and-conquer and on inclusion–exclusion characterizations. We show that the Exact Satisfiability problem of size l with m clauses can be solved in time 2 m lO(1) and polynomial space. The same bounds hold for counting the number of solutions. As a special case, we can count the number of perfect matchings in an n-vertex graph in time 2nn O(1) and polynomial space. We also show how to count the number of perfect matchings in time O(1.732n) and exponential space. We give a number of examples where the running time can be further improved if the hypergraph corresponding to the set cover instance has low pathwidth. This yields exponential-time algorithms for counting k-dimensional matchings, Exact Uniform Set Cover, Clique Partition, and Minimum Dominating Set in graphs of degree at most three. We extend the analysis to a number of related problems such as TSP and Chromatic Number.