Abstract
In this paper we describe recent developments in the theory and algorithm design of combinatorial optimization that are related to questions concerning ground states of spin glasses. In particular, we outline an approach, based on polyhedral combinatorics, that has led to the implementation of a cutting plane method for calculating exact ground states of spin glasses in the Ising model. With this method exact ground states for planar grids of size up to 40 x 40 with periodic boundary conditions and exterior magnetic field can be determined in reasonable running times.
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