GPU-LSolve: An Efficient GPU-Based Laplacian Solver for Million-Scale Graphs

Breaking from the general run of Laplacian solvers that depend on algebraic primitives, we present the first GPU implementation of a message-passing-based solver. Our solver called GPU-LSolve, implements a randomized algorithm that simulates a queueing network where some nodes act as sources that generate messages and one node acts as a sink that removes messages from the network. The steady state of this network provides a solution for the Laplacian system of equations. We show how the simplicity of the primitives of this algorithm can be leveraged in a G PU setting to provide an efficient implementation that can solve Laplacian systems on million-scale graphs. Our solver takes advantage of GPU parallelism through sorting and key-value reduction. We have provided an extensive experimental evaluation on real data sets against several recently developed solvers. It is shown from the results that the presented solver does not suffer much in terms of memory footprint and execution time.