Parallel incremental graph partitioning using linear programming

Abstract

Partitioning graphs into equally large groups of nodes while minimizing the number of edges between different groups is an extremely important problem in parallel computing. For instance, efficiently parallelizing several scientific and engineering applications requires the partitioning of data or tasks among processors such that the computational load on each node is roughly the same, while communication is minimized. Obtaining exact solutions is computationally intractable, since graph-partitioning is an NP-complete.For a large class of irregular and adaptive data parallel applications (such as adaptive meshes), the computational structure changes from one phase to another in an incremental fashion. In incremental graph-partitioning problems the partitioning of the graph needs to be updated as the graph changes over time; a small number of nodes or edges may be added or deleted at any given instant.In this paper we use a linear programming-based method to solve the incremental graph partitioning problem. All the steps used by our method are inherently parallel and hence our approach can be easily parallelized. By using an initial solution for the graph partitions derived from recursive spectral bisection-based methods, our methods can achieve repartitioning at considerably lower cost than can be obtained by applying recursive spectral bisection from scratch. Further, the quality of the partitioning achieved is comparable to that achieved by applying recursive spectral bisection to the incremental graphs from scratch.