Abstract
A versatile family of interconnection networks alternative to hypercubes, called Metacubes, has been proposed for building extremely large scale multiprocessor systems with a small number of links per node. A Metacube MC(k, m) connects 22 km + k nodes with only k + m links per node. Metacube can be used to build parallel computing systems of very large scale with a small number of links per node. In this paper, we propose a new presentation of Metacube for algorithmic design. Based on the new presentation, we give efficient algorithms for parallel prefix computation and parallel sorting on Metacubes, respectively. The algorithm for prefix computation runs in 2 km (k + 1) + k communication steps and 2 k + 1 m + 2k computation steps on MC(k, m). The sort algorithm runs in O(2 km + k)2 computation steps and O(2 km (2k + 1) + k)2 communication steps on MC(k, m).
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