Colin McQuillan

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An important tool in the study of the complexity of Constraint Satisfaction Problems (CSPs) is the notion of a relational clone, which is the set of all relations expressible using primitive positive formulas over a particular set of base relations. Post's lattice gives a complete classification of all Boolean relational clones, and this has been used to(More)
We give an FPRAS for Holant problems with parity constraints and not-all-equal constraints , a generalisation of the problem of counting sink-free-orientations. The approach combines a sampler for near-assignments of " windable " functions – using the cycle-unwinding canonical paths technique of Jerrum and Sinclair – with a bound on the weight of(More)
We study the complexity of approximation for a weighted counting constraint satisfaction problem #CSP(F). In the conservative case, where F contains all unary functions, a classification is known for the Boolean domain. We give a classification for problems with general finite domain. We define weak log-modularity and weak log-supermodularity, and show that(More)
Given a symmetric DxD matrix M over {0, 1, *}, a list M-partition of a graph G is a partition of the vertices of G into D parts which are associated with the rows of M. The part of each vertex is chosen from a given list in such a way that no edge of G is mapped to a 0 in M and no non-edge of G is mapped to a 1 in M. Many important graph-theoretic(More)
We consider the problem of approximating the partition function of the hard-core model on planar graphs of degree at most 4. We show that when the activity λ is sufficiently large, there is no fully polynomial randomised approximation scheme for evaluating the partition function unless NP = RP. The result extends to a nearby region of the parameter space in(More)
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