RAMA: A Rapid Multicut Algorithm on GPU

Abstract

We propose a highly parallel primal-dual algorithm for the multicut (a.k.a. correlation clustering) problem, a classical graph clustering problem widely used in machine learning and computer vision. Our algorithm consists of three steps executed recursively: (1) Finding conflicted cycles that correspond to violated inequalities of the underlying multicut relaxation, (2) Performing message passing between the edges and cycles to optimize the Lagrange relaxation coming from the found violated cycles producing reduced costs and (3) Contracting edges with high reduced costs through matrix-matrix multiplications.Our algorithm produces primal solutions and dual lower bounds that estimate the distance to optimum. We implement our algorithm on GPUs and show resulting one to two order-of-magnitudes improvements in execution speed without sacrificing solution quality compared to traditional serial algorithms that run on CPUs. We can solve very large scale benchmark problems with up to O(10 8 ) variables in a few seconds with small primal-dual gaps. We make our code available at https://github.com/ pawelswoboda/RAMA.

FastDOG: Fast Discrete Optimization on GPU

“…FastDOG [1,45,54,61] several hundred works Figure 1. Qualitative comparison of ILP solvers for structured prediction.…”

“…For Maximum-A-Posteriori inference in Markov Random Fields [45,61] proposed a dual block coordinate ascent algorithm for sparse and [54] for dense graphs. For multicut a primal-dual algorithm has been proposed in [1]. Max-flow GPU implementations have been investigated in [56,60].…”

“…message passing) algorithms which optimize a Lagrange decomposition. Solvers have been developed for MRFs [16,27,28,33,34,39,44,54,55,57,58], graph matching [50,51,62], multicut [1,36,49], multiple object tracking [24] and cell tracking [21]. Most of the above algorithms require a sequential computation of update steps.…”

“…To our knowledge there exists no practical and general GPU-based optimization routine and only a few solvers for narrow problem classes have been made GPU-compatible e.g. [1,45,54,61]. This, and the superlinear runtime complexity of general ILP solvers has hindered application of ILPs in large structured prediction problems, necessitating either restriction to at most medium problem sizes or difficult and time-consuming development of specialized CPU GPU…”