Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Reduction algorithms for graphs of small treewidth
Information and Computation
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
Complexity of domination-type problems in graphs
Nordic Journal of Computing
Dominating sets in planar graphs: branch-width and exponential speed-up
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Dynamic programming and fast matrix multiplication
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Parameterized and Exact Computation
Efficient exact algorithms on planar graphs: exploiting sphere cut branch decompositions
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Parameterized complexity of generalized domination problems
Discrete Applied Mathematics
Fixed-Parameter tractability of treewidth and pathwidth
The Multivariate Algorithmic Revolution and Beyond
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We combine two techniques recently introduced to obtain faster dynamic programming algorithms for optimization problems on graph decompositions. The unification of generalized fast subset convolution and fast matrix multiplication yields significant improvements to the running time of previous algorithms for several optimization problems. As an example, we give an O*(3ω/2k) time algorithm for Minimum Dominating Set on graphs of branchwidth k, improving on the previous O*(4k) algorithm. Here ω is the exponent in the running time of the best matrix multiplication algorithm (currently ω k, we improve from O*(8k) to O*(4k). We also obtain an algorithm for counting the number of perfect matchings of a graph, given a branch decomposition of width k, that runs in time O*(2ω/2k). Generalizing these approaches, we obtain faster algorithms for all so-called [ρ, σ]-domination problems on branch decompositions if ρ and ρ are finite or cofinite. The algorithms presented in this paper either attain or are very close to natural lower bounds for these problems.