A graph-oriented mapping strategy for a hypercube

The mapping problem is the problem of implementing a computational task on a target architecture in order to maximize some performance metric. For a hypercube-interconnected multiprocessor, the mapping problem arises when the topology of a task graph is different from a hypercube. It is desirable to find a mapping of tasks to processors that minimizes average path length and hence interprocessor communication. The problem of finding an optimal mapping, however, has been proven to be NP-complete. Several different approaches have been taken to discover suitable mappings for a variety of target architectures. Since the mapping problem is NP-complete, approximation algorithms are used to find good mappings instead of optimal ones. Usually, greedy and/or local search algorithms are introduced to approximate the optimal solutions. This paper presents a greedy mapping algorithm for hypercube interconnection structures, which utilizes the graph-oriented mapping strategy to map a communication graph to a hypercube. The strategy is compared to previous strategies for attacking the mapping problem. A simulation is performed to estimate both the worst-case bounds for the greedy mapping strategy and the average performance.