Review for NeurIPS paper: Strongly local p-norm-cut algorithms for semi-supervised learning and local graph clustering

Summary and Contributions: This paper introduces a new class of algorithms for local graph clustering, based on Lp objectives (for p 2) rather than the standard L2 (used in reference works like Anderson-Chang-Lang), or L_infinity (which corresponds to minimum cut). The authors make a clear point that the p 2 regime corresponds to the primal objective which optimizes in the space of flows, whose dual problem corresponds to optimizing an Lq norm (1 q 2) in the space of cuts. For the purpose of this paper, they stick to the cut problem, since it is more naturally connected to the algorithm described here. Essentially, the presented algorithm is a generalization of ACL for Lq norms. It performs a sequence of steps, in each step, it picks a node with excess residual and performs "push" operation.