Hypergraph-based Dynamic Partitioning and Load Balancing

1.1 INTRODUCTION An important component of parallel scientific computing is the assignment of work to processors. This assignment problem is also known as partitioning or mapping. The goal of the assignment problem is to find a task-to-processor mapping that will minimize the total execution time. Although efficient optimal solutions for certain restricted variations, such as chain-or tree-structured programs exist [21], the general problem is NP-hard [28]. We consider this general version where any task can potentially be assigned to any processor. In the literature, the task-to-processor assignment problem is usually solved by a two-step approach: first tasks are partitioned into load-balanced clusters of tasks, then these clusters are mapped to processors. In the partitioning step, a common goal is to minimize the interprocessor communication while maintaining a computational load balance among processors. Partitioning occurs at the start of a computation (static partitioning), but often, reassignment of work is done during a computation (dynamic partitioning or repartitioning) as the work distribution changes over the course of the computation. Repar-titioning usually includes both partitioning and mapping. While distinction between partitioning, load balancing and mapping can be made as described, throughout this chapter we will use the terms interchangeably to refer the assignment problem. We will assume that the mapping step of the two-step approach either is trivial, or inherent in the partitioning approach. Dynamic partitioning is an important feature in parallel adaptive computations [9]. Even if the original problem is well balanced, e.g., by using graph or hypergraph partitioning, the computation may become unbalanced over time due to dynamic changes. A classic example is simulation based on adap-tive mesh refinement, in which the computational mesh changes between time steps. The difference is often small, but over time, the cumulative change in the mesh becomes significant. Therefore dynamic load balancing may be required periodically to re-balance the application, that is, move data among processors to improve the load balance. Dynamic load balancing or repartitioning is a well studied that has multiple objectives with complicated trade-offs among them: 1. good load balance in the new data distribution; 2. low communication cost within the application (as determined by the new distribution); 3. low data migration cost to move data from the old to the new distribution ; and 4. short repartitioning time. Total execution time is commonly modeled [26, 34] as follows to account for these objectives: t tot = α(t comp + t comm) …