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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper presents a novel algorithm to solve the balanced k-cut problem. The k-cut criterion is defined by using the Lovasz extension of a set function. A relaxation of balanced k-cut functionals can be formulated using Lovasz extensions of cuts and of normalizing constraints. The appealing feature of this relaxation is the connection between convex Lovasz extensions and submodular set functions. The authors propose an algorithm that minimizes a sum of auxiliary variables that are lower-bounded by ratios.