Abstract
We show that the partitions of an n-element set into k members of a given set family can be counted in time O((2 − ε)n), where ε> 0 depends only on the maximum size among the members of the family. Specifically, we give a simple combinatorial algorithm that counts the perfect matchings in a given graph on n vertices in time O(poly(n)ϕ n), where ϕ = 1.618... is the golden ratio; this improves a previous bound based on fast matrix multiplication.
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Koivisto, M. (2009). Partitioning into Sets of Bounded Cardinality. In: Chen, J., Fomin, F.V. (eds) Parameterized and Exact Computation. IWPEC 2009. Lecture Notes in Computer Science, vol 5917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11269-0_21
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DOI: https://doi.org/10.1007/978-3-642-11269-0_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11268-3
Online ISBN: 978-3-642-11269-0
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