Boolean N-cube Research Articles

The number of spanning trees of the generalized Boolean n-cube network

In this paper, the well-known Boolean n-cube networks are extended to the generalized Boolean n-cube networks which are based on a mixed radix number system. Although a classic theorem—the matrix tree theorem—can compute the number of spanning trees of any graph, however, we derive a simple formula for this general structure.

Graph theoretic reliability analysis for the Boolean n cube networks

Two graph-theoretic results concerning Boolean n-cube network reliability are presented. First, a simple formula for the number of spanning trees of the Boolean n-cube network is derived. As a result, the reliability function for large failure rate can be readily computed. Second, the Boolean n-cube network is proved to have the super-line-connectivity property. Thus the number of line-disconnecting sets (a set of lines the removal of which results in a disconnected or trivial graph) or order lambda for the Boolean n-cube network is equal to 2/sup n/.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Solving banded systems on a parallel processor

In this paper we examine ways of solving dense, banded systems on different parallel processors. We start with some considerations for processors with vector instructions, then discuss various algorithms for the solution of large, dense, banded systems on a parallel processor. We analyze the behavior of the parallel algorithms on distributed-storage architectures configured as rings, two-dimensional meshes with end-around connections (tori), boolean n-cube configured architectures, and bus-based and switch-based machines with shared storage. We also present measurements for two bus-based architectures with shared storage, namely, the Alliant FX/8 and the Sequent Balance 21000.

Generalized Hypercube and Hyperbus Structures for a Computer Network

A general class of hypercube structures is presented in this paper for interconnecting a network of microcomputers in parallel and distributed environments. The interconnection is based on a mixed radix number system and the technique results in a variety of hypercube structures for a given number of processors N, depending on the desired diameter of the network. A cost optimal realization is obtained through a process of discrete optimization. The performance of such a structure is compared to that of other existing hypercube structures such as Boolean n-cube and nearest neighbor mesh computers.

An Efficient Approach for Fault Diagnosis in a Boolean n-Cube Array of Microprocessors

In this correspondence a O(n3)-time algorithm for fault diagnosis in an n-cube connected array of processors is presented using the notion of candidate processors and syndrome information digraphs.