Optimal task assignment in heterogeneous computing systems

Abstract

Distributed systems comprising networked heterogeneous workstations are now considered to be a viable choice for high-performance computing. For achieving a fast response time from such systems, an efficient assignment of the application tasks to the processors is imperative. The general assignment problem is known to be NP-hard, except in a few special cases with strict assumptions. While a large number of heuristic techniques have been suggested in the literature that can yield sub-optimal solutions in a reasonable amount of time, we aim to develop techniques for optimal solutions under relaxed assumptions. The basis of our research is a best-first search technique known as the A* algorithm from the area of artificial intelligence. The original search technique guarantees an optimal solution but is not feasible for problems of practically large sizes due to its high time and space complexity. We propose a number of algorithms based around the A* technique. The proposed algorithms also yield optimal solutions but are considerably faster. The first algorithm solves the assignment problem by using parallel processing. Parallelizing the assignment algorithm is a natural way to lower the time complexity, and we believe our algorithm to be novel in this regard. The second algorithm is based on a clustering based pre-processing technique that merges the high affinity tasks. Clustering reduces the problem size, which in turn reduces the state-space for the assignment algorithm. We also propose three heuristics which do not guarantee optimal solutions but provide near-optimal solutions and are considerably faster. By using our parallel formulation, the proposed clustering technique and the heuristics can also be parallelized to further improve their time complexity.