Planar Cycle Covering Graphs

We describe a new variational lower-bound on the minimum energy configuration of a planar binary Markov Random Field (MRF). Our method is based on adding auxiliary nodes to every face of a planar embedding of the graph in order to capture the effect of unary potentials. A ground state of the resulting approximation can be computed efficiently by reduction to minimum-weight perfect matching. We show that optimization of variational parameters achieves the same lower-bound as dual-decomposition into the set of all cycles of the original graph. We demonstrate that our variational optimization converges quickly and provides highquality solutions to hard combinatorial problems 10-100x faster than competing algorithms that optimize the same bound.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Julian Yarkony, Alexander T. Ihler, Charless C. Fowlkes
• Keywords: CORR 2011, Education, Minimum Energy Configuration, Planar Binary Markov, Variational