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Issue No. 09 - Sept. (2013 vol. 35)
ISSN: 0162-8828
pp: 2304-2306
B. Flach , Fac. of Electr. Eng., Czech Tech. Univ., Prague, Czech Republic
The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising models with homogeneous pairwise potentials but arbitrary (inhomogeneous) unary potentials. Similarly, the partition function and marginal probabilities can be computed in polynomial time for random fields on complete bipartite graphs, provided they have homogeneous pairwise potentials. We expect that these tractable classes of large-scale random fields can be very useful for the evaluation of approximation algorithms by providing exact error estimates.
Labeling, Computational modeling, Bipartite graph, Partitioning algorithms, Time complexity, Approximation methods, Polynomials

B. Flach, "A Class of Random Fields on Complete Graphs with Tractable Partition Function," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 35, no. 9, pp. 2304-2306, 2013.
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