Balancing Maximal Independent Sets using Hadoop

Abstract

Given a graph G = (V, E), an independent set I is a subset of vertices, such that no two vertex in I share a common edge. A maximal independent set (MIS) is an independent set such that there is no way we can add any other vertex such that the property of independent set remains intact. Different MIS heuristics are used in parallel applications for identifying the subset of independent tasks. Traditional MIS heuristics aim to generate minimum number of MIS i.e. number of parallel steps for the particular applications. However, if MIS produced have skewed sizes, hardware resource utilization becomes inefficient. Parallel computing has become a key feature for improving performance in these days. A task is broken down into various subtasks and each sub-task is executed in parallel on various processors. This is where generating and balancing the maximal independent sets come into play. In this paper, in the context of parallel application, we have proposed a heuristic for balancing the maximal independent sets using Hadoop after dividing the graph into various maximal independent sets. We have verified through experiment that our heuristic balances MIS' without much increasing the number of MIS generated.