Exact Covers via Determinants

Given a k-uniform hypergraph on n vertices, partitioned in k equal parts such that every hyperedge includes one vertex from each part, the k-Dimensional Matching problem asks whether there is a disjoint collection of the hyperedges which covers all vertices. We show it can be solved by a randomized polynomial space algorithm in O∗ (2n(k−2)/k ) time. The O∗ () notation hides factors polynomial in n and k. The general Exact Cover by k-Sets problem asks the same when the partition constraint is dropped and arbitrary hyperedges of cardinality k are permitted. We show it can be solved by a randomized polynomial space algorithm in O∗ (cn

• Type: Conference
• Year: 2010
• Where: STACS
• Authors: Andreas Björklund
• Keywords: K-dimensional Matching Problem, Notation Hides Factors, Polynomial Space Algorithm, STACS 2010, Theoretical Computer Science