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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)

- Xi Chen, Martin E. Dyer, Leslie Ann Goldberg, Mark Jerrum, Pinyan Lu, Colin McQuillan +1 other
- STACS
- 2013

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 D × D 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)

- Andris Ambainis, Andreas Göbel, Leslie Ann Goldberg, Colin McQuillan, David Richerby, Tomoyuki Yamakami +13 others
- 2014

A counting constraint satisfaction problem (#CSP) asks for the number of ways to satisfy a given list of constraints, drawn from a fixed constraint language Γ. We study how hard it is to evaluate this number approximately. There is an interesting partial classification, due to Dyer, Goldberg, Jalsenius and Richerby [DGJR10], of Boolean constraint languages… (More)

The material in this note is superceded by [2].

- Colin McQuillan
- 2013

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