Huang, Ke.

We propose the balanced hypercube (BH), which is a variant of the standard hypercube (Q), as a multicomputer topological structure. An n-dimensional balanced hypercube BHn has the same desirable topological properties of the 2n-dimensional standard hypercube Q2n such as size (2^2n nodes and n2^2n edges), regularity and symmetry, connectivity (2n node-disjoint pathes between any pair of nodes), and diameter (2n when n = 1 or n is even). Moreover, BHn has smaller diameter (2n-1) than Qn's (2n) when n is odd other than 1. In addition, BHn is load balanced, i.e., for every node v of BHn, there exists another node v', called v's matching node, such that v and v' share the same adjacent node set. Therefore, BHn has a desirable fault tolerance feature: when a node v fails, we can simply shift the job execution on v to its matching node v' and the communication pattern between jobs remains the same. In this dissertation, we study the topological properties of BHn and explore its fault tolerance feature. Other design issues are considered, such as communication primitives, capability of simulating other multicomputer systems through graph embedding, resource placement. and VLSI/WSI layout. Finally, the use of BHn is illustrated by an application.