Hypergraph Partitioning in the Cloud

Abstract

The thesis investigates the partitioning and load balancing problem which has many applications in High Performance Computing (HPC). The application to be partitioned is described with a graph or hypergraph. The latter is of greater interest as hypergraphs, compared to graphs, have a more general structure and can be used to model more complex relationships between groups of objects such as non-symmetric dependencies. Optimal graph and hypergraph partitioning is known to be NP-Hard but good polynomial time heuristic algorithms have been proposed.

In this thesis, we propose two multi-level hypergraph partitioning algorithms. The algorithms are based on rough set clustering techniques. The first algorithm, which is a serial algorithm, obtains high quality partitionings and improves the partitioning cut by up to 71 compared to the state-of-the-art serial hypergraph partitioning algorithms. Furthermore, the capacity of serial algorithms is limited due to the rapid growth of problem sizes of distributed applications. Consequently, we also propose a parallel hypergraph partitioning algorithm. Considering the generality of the hypergraph model, designing a parallel algorithm is difficult and the available parallel hypergraph algorithms offer less scalability compared to their graph counterparts. The issue is twofold: the parallel algorithm and the complexity of the hypergraph structure. Our parallel algorithm provides a trade-off between global and local vertex clustering decisions. By employing novel techniques and approaches, our algorithm achieves better scalability than the state-of-the-art parallel hypergraph partitioner in the Zoltan tool on a set of benchmarks, especially ones with irregular structure.

Furthermore, recent advances in cloud computing and the services they provide have led to a trend in moving HPC and large scale distributed applications into the cloud. Despite its advantages, some aspects of the cloud, such as limited network resources, present a challenge to running communication-intensive applications and make them non-scalable in the cloud. While hypergraph partitioning is proposed as a solution for decreasing the communication overhead within parallel distributed applications, it can also offer advantages for running these applications in the cloud. The partitioning is usually done as a pre-processing step before running the parallel application. As parallel hypergraph partitioning itself is a communication-intensive operation, running it in the cloud is hard and suffers from poor scalability. The thesis also investigates the scalability of parallel hypergraph partitioning algorithms in the cloud, the challenges they present, and proposes solutions to improve the cost/performance ratio for running the partitioning problem in the cloud.

Our algorithms are implemented as a new hypergraph partitioning package within Zoltan. It is an open source Linux-based toolkit for parallel partitioning, load balancing and data-management designed at Sandia National Labs. The algorithms are known as FEHG and PFEHG algorithms.