An Improved Hill Climbing Algorithm for Graph Partitioning

Abstract

Abstract Graph partitioning is an NP-hard combinatorial optimization problem, and is a fundamental step in distributing workloads on parallel compute systems, circuit placement, and sparse matrix reordering. The proposed heuristic algorithms such as streaming graph partitioning provide solutions to large-scale graph in a reasonable amount of time. However, the ability of breaking out of local minima in existing these methods is very limited as they are simple in reflecting the connectivity between vertices in real graphs with power-law distribution characteristic. As hill climbing algorithm is a local search method, it can be adopted to improve the result of graph partitioning. However, directly adopting the existing hill climbing algorithm to graph partitioning will result in local minima and poor convergence speed during the iterative process. In this paper, we propose an improved hill climbing graph partitioning algorithm based on clustering. Instead of taking a single vertex as a basic unit, the proposed method considers a cluster consisting of a series of vertices as a hill to move during each iteration. The method uses a new metric that considers both balance and edgecuts to look for the most beneficial cluster as the hill. With these improvements, the method provides a strong power to break out of local minima and achieve an adaptive tradeoff between balance and edgecuts. Experimental results on real-world graphs show that the proposed algorithm substantially reduces edgecuts within a controlled imbalance range.