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Title: The computational complexity of approximation of partition functions
Author: McQuillan, Colin
Awarding Body: University of Liverpool
Current Institution: University of Liverpool
Date of Award: 2013
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This thesis studies the computational complexity of approximately evaluating partition functions. For various classes of partition functions, we investigate whether there is an FPRAS: a fully polynomial randomised approximation scheme. In many of these settings we also study 'expressibility', a simple notion of defining a constraint by combining other constraints, and we show that the results cannot be extended by expressibility reductions alone. The main contributions are: • We show that there is no FPRAS for evaluating the partition function of the hard-core gas model on planar graphs at fugacity 312, unless RP = NP. • We generalise an argument of Jerrum and Sinclair to give FPRASes for a large class of degree-two Boolean #CSPs. • We initiate the classification of degree-two Boolean #CSPs where the constraint language consists of a single arity 3 relation. • We show that the complexity of approximately counting downsets in directed acyclic graphs is not affected by restricting to graphs of maximum degree three. • We classify the complexity of degree-two #CSPs with Boolean relations and weights on variables. • We classify the complexity of the problem #CSP(F) for arbitrary finite domains when enough non-negative-valued arity 1 functions are in the constraint language. • We show that not all log-supermodular functions can be expressed by binary logsupermodular functions in the context of #CSPs.
Supervisor: Goldberg, Leslie Anne; Martin, Russell Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA75 Electronic computers. Computer science