Partitioning into Sets of Bounded Cardinality

Authors:
Mikko Koivisto
Affiliations:
Helsinki Institute for Information Technology HIIT, Department of Computer Science, University of Helsinki, Finland FI-00014
Venue:
Parameterized and Exact Computation
Year:
2009

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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 驴驴) n ), where 驴 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.