OPERATIONALLY ENHANCED FOLDED HYPERCUBES

Abstract

Recently, several variations of the hypercube have been proposed to enhance its performance and reliability. The folded hypercube is one of these variations, in which an extra link is added to each node providing a direct connection to the node located farthest from it. In this short note, we propose a new operation mode of folded hypercube to enhance its performance and fault-tolerance. There are (n+1k) regular k-cubes within a folded hypercube of dimension n, denoted by FQ(n). We introduce another type of hypercube, called the twisted hypercube, to improve the performance and fault tolerance of the folded hypercube. The problems of finding a subcube of given size in an FQ(n) and routing messages within the subcube are addressed for the proposed operation mode. The advantages of the proposed operation mode over the regular-hypercube operation mode are analyzed in terms of dependability and robustness. The proposed operation mode is shown to make significant improvements over the regular-hypercube operation mode in both dependability and robustness. Because the new operation mode can be applied to only an (n - 1)-subcube level for a given FQ(n), we present a general form of folded hypercube, thus enhancing the availability of subcubes of any dimension m < n.