Partitioning into Sets of Bounded Cardinality [chapter]

Mikko Koivisto
2009 Lecture Notes in Computer Science  
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− ) n ), 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 n ), where ϕ = 1.618 . . . is the golden ratio; this improves a previous bound based on fast matrix multiplication.
doi:10.1007/978-3-642-11269-0_21 fatcat:abr6k7xxsncepfcdtnl4bplkau