Efficient GPU Implementation for Solving the Maximum Independent Set Problem

Abstract

An independent set of a graph is a subset of the nodes such that no two nodes in it are adjacent. The maximum independent set (MIS) problem is an optimization problem to find an independent set with the largest possible number of nodes. Since the MIS problem is NP-hard, finding optimal solutions for large graphs is quite difficult and approximation or heuristic algorithms are used to find independent sets as large as possible. The main contribution of this paper is to present an annealing-based parallel heuristic algorithm for finding approximate solutions for the MIS problem. We have implemented it to run on a computing server with multiple GPUs. The performance of our GPU implementation is compared with the other approaches including a GPU QUBO solver, Gurobi optimizer running on an Intel multicore server, and D-wave 2000Q quantum annealer. The experimental results for random graphs show that our GPU implementation for the MIS problem can find optimal or better solutions than the other approaches. In particular, for small random graphs with 128 nodes or less, our GPU implementation can find optimal solutions of the MIS problem in less than 20µs, while the other approaches take more than 10ms. Further, for large regular random graphs with 32M nodes, our GPU implementation can obtain 22.6%-38.5% larger independent sets. Thus, our parallel GPU implementation for solving the MIS problem is a potent approach to solve the MIS problem.