Partitioning into Sets of Bounded Cardinality
نویسنده
چکیده
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− )), where > 0 depends only on the maximum size among the members of the family. Specifically, we give a simple combinatorial algorithm that counts perfect matchings in a given graph on n vertices in time O(poly(n)φ), where φ = 1.618 . . . is the golden ratio; this improves a previous bound based on fast matrix multiplication.
منابع مشابه
A note on triangle partitions
Koivisto studied the partitioning of sets of bounded cardinality. We improve his time analysis somewhat, for the special case of triangle partitions, and obtain a slight improvement.
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