Graph Partitioning Using Heuristic Kernighan-Lin Algorithm for Parallel Computing

Abstract

The goal of parallel computing is to distribute the load on available processors such that all processors should be utilized in a fair manner. This minimizes the overall execution time required to execute a complex task. So, the load balancing issue becomes an important aspect of parallel computing. It is abstracted as a graph partitioning problem in which the nodes represent computation cost, edges represent communication cost, and number of partitions should be equal to number of available processing units. So, the objective is to cut the graph into k-partitions such that—(i) total node weight should be equal for each partition and—(ii) minimize total edge weight across the partitions. A heuristic Kernighan-Lin graph partitioning algorithm for two-way partitioning is evaluated in this paper. It starts with an initial random graph partition and consecutively exchanges the nodes between partitions, determines cut size at each stage and saves the minimum cut found so far. After the desired number of swaps has been performed, the saved minimum cut will give optimal partitions. The graph data for experimental work is obtained from DIMACS tenth implementation challenge Web site. The experimental results show minimum cut-cost with respect to balance constraint. The results are compared with ground truth results for validation.