29 Jan 10:15 Mikko Koivisto: Partitioning into Sets of Bounded Cardinality

HIIT seminar, Friday Jan 29, 10:15 a.m. (coffee from 10), Exactum B222

Dr. Mikko Koivisto
Helsinki Institute for Information Technology HIIT Department of Computer Science University of Helsinki

Partitioning into Sets of Bounded Cardinality

Abstract:
Research on moderately exponential time algorithms often deals with well-studied combinatorial objects, such as Hamiltonian cycles, dominating sets, graph colorings, and perfect matchings. In this talk, I will present a recent result that concerns the latter two, or more generally, set partitions.

We show that the partitions of an n-element set into k members of a given set family can be counted in time O(C^n), where C < 2 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) G^n), where G = 1.618... is the golden ratio; this improves a previous bound based on fast matrix multiplication.


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