2021/03/05 by Kyriakos Axiotis, Axiotis, Kyriakos, Adam Karczmarz +7
Computer Science · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Cryptography and Data Security #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Machine Learning (cs.LG) #cs.DS #cs.LG
paper · pdf · doi:10.48550/arxiv.2103.03868
arxiv created 2021/03/05 · openalex publication_date 2021/03/05 · arxiv updated 2021/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper bridges discrete and continuous optimization approaches for decomposable submodular function minimization, in both the standard and parametric settings. We provide improved running times for this problem by reducing it to a number of calls to a maximum flow oracle. When each function in the decomposition acts on O(1) elements of the ground set V and is polynomially bounded, our running time is up to polylogarithmic factors equal to that of solving maximum flow in a sparse graph with O(\vert V \vert) vertices and polynomial integral capacities. We achieve this by providing a simple iterative method which can optimize to high precision any convex function defined on the submodular base polytope, provided we can efficiently minimize it on the base polytope corresponding to the cut function of a certain graph that we construct. We solve this minimization problem by lifting the solutions of a parametric cut problem, which we obtain via a new efficient combinatorial reduction to maximum flow. This reduction is of independent interest and implies some previously unknown bounds for the parametric minimum s,t-cut problem in multiple settings.