Graph Cuts with Interacting Edge Costs - Examples, Approximations, and Algorithms

Graphs find applications as a representation of a multitude of problems in mathematics, discrete optimization, and technology. In many cases, this representation leads to very practical algorithms. In some settings, however, a (sparse) graph is not expressive enough. Such limitations are often due to the fact that the edges (pair-wise interactions of nodes) are independent. This paper studies an extension that remedies many of these shortcomings: instead of a sum of edge weights, we allow a (non-linear) submodular function over graph edges, which leads to a coupling of the edges. In particular, we focus on cut problems with such interacting edge weights. We survey applications and present algorithms and empirical results.