Dynamic Programming on Tree Decompositions Using Generalised Fast Subset Convolution

@inproceedings{Rooij2009DynamicPO,
  title={Dynamic Programming on Tree Decompositions Using Generalised Fast Subset Convolution},
  author={Johan M. M. van Rooij and Hans L. Bodlaender and Peter Rossmanith},
  booktitle={ESA},
  year={2009}
}
In this paper, we show that algorithms on tree decompositions can be made faster with the use of generalisations of fast subset convolution. Amongst others, this gives algorithms that, for a graph, given with a tree decomposition of width k, solve the dominated set problem in O(nk3) time and the problem to count the number of perfect matchings in O∗(2k) time. Using a generalisation of fast subset convolution, we obtain faster algorithms for all [ρ, σ]-domination problems with finite or cofinite… CONTINUE READING

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