Scalable Load Balancing Techniques for Parallel Computers

In this paper we analyze the scalability of a number of load balancing algorithms which can be applied to problems that have the following characteristics : the work done by a processor can be partitioned into independent work pieces; the work pieces are of highly variable sizes; and it is not possible (or very diicult) to estimate the size of total work at a given processor. Such problems require a load balancing scheme that distributes the work dynamically among diierent processors. Our goal here is to determine the most scalable load balancing schemes for diierent archi-tectures such as hypercube, mesh and network of workstations. For each of these architectures, we establish lower bounds on the scalability of any possible load balancing scheme. We present the scalability analysis of a number of load balancing schemes that have not been analyzed before. This gives us valuable insights into their relative performance for diierent problem and architectural characteristics. For each of these architectures, we are able to determine near optimal load balancing schemes. Results obtained from implementation of these schemes in the context of the Tautology Veriication problem on the Ncube/2 TM1 multicomputer are used to validate our theoretical results for the hypercube architecture. These results also demonstrate the accuracy and viability of our framework for scalability analysis.