The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Apolarity and canonical forms for homogeneous polynomials
European Journal of Combinatorics - Special issue dedicated to Bernt Lindstro¨m
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
The Parameterized Complexity of Counting Problems
SIAM Journal on Computing
Holographic Algorithms (Extended Abstract)
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Finding, minimizing, and counting weighted subgraphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Weighted counting of k-matchings is #w[1]-hard
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
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We prove $\sharp$W[1]-hardness of the following parameterized counting problem: Given a simple undirected graph G and a parameter k∈ℕ, compute the number of matchings of size k in G. It is known from [1] that, given an edge-weighted graph G, computing a particular weighted sum over the matchings in G is $\sharp$W[1]-hard. In the present paper, we exhibit a reduction that does not require weights. This solves an open problem from [5] and adds a natural parameterized counting problem to the scarce list of $\sharp$W[1]-hard problems. Since the classical version of this problem is well-studied, we believe that our result facilitates future $\sharp$W[1]-hardness proofs for other problems.