Inclusion and exclusion algorithm for the Hamiltonian Path Problem
Information Processing Letters
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
An improved exact algorithm for the domatic number problem
Information Processing Letters
An exact algorithm for the minimum dominating clique problem
Theoretical Computer Science
Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications
ACM Transactions on Algorithms (TALG)
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
Set Partitioning via Inclusion-Exclusion
SIAM Journal on Computing
Exact Algorithms for Dominating Clique Problems
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
An exact 2.9416n algorithm for the three domatic number problem
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Algorithmics in exponential time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Finding a minimum feedback vertex set in time O(1.7548n)
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Combinatorial Optimization on Graphs of Bounded Treewidth
The Computer Journal
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Inclusion/exclusion and measure and conquer are two of the most important recent new developments in the field of exact exponential time algorithms. Algorithms that combine both techniques have been found very recently, but thus far always use exponential space. In this paper, we try to obtain fast exponential time algorithms for graph domination problems using only polynomial space. Using a novel treewidth based annotation procedure to deal with sparse instances, we give an algorithm that counts the number of dominating sets of each size κ in a graph in $\mathcal{O}(1.5673^n)$ time and polynomial space. We also give an algorithm for the domatic number problem running in $\mathcal{O}O(2.7139^n)$ time and polynomial space.