Embedding tree structures in MPCs: application to the MasPar MP-2

Abstract

Trees are an important class of computational structures due to their favourable property of logarithmic path from the root to any leaf element. Mapping problems arise when the tree structure differs from the processor interconnection of the parallel computer. The MasPar's MP-2 is a massively parallel computer where processors are interconnected via the X-Net neighborhood two-dimensional mesh and the global multistage crossbar router network. Novel mapping schemes for trees on the MasPar's MP-2 two-dimensional mesh and on the two-dimensional mesh together with the MasPar's MP-2 multistage crossbar network are proposed here. Appropriate algorithms of the mapping scheme on the two-dimensional mesh (or grid) are presented and shown to be superior over known mappings on square array (or grids). These mapping schemes are well suited for massively parallel systems which focus on data parallelism. This parallelism comes from simultaneous operations across large sets of data. It is the data parallelism style which opposes the control parallel style used in multiprocessing.<>