Distributed subcube identification algorithms for reliable hypercubes

The proposed all-optical 2-D switching networks are (i) M×N-gon prism switches ($\text{M⩾2,}\text{N⩾3}$) and (ii) 3-D grids of any geometry N⩾3. For the routing we assume (1) the projection of the spatial architectures onto plane graphs (2) the embedding of the latter guest graphs into (in)complete host hypercubes (N=4) and generally, into N-cube networks (N⩾3) and (3) routing by means of the cube algorithms of the host. By the embedding mainly faulty cubes (synonyms: injured cubes, incomplete cubes) arise which complicate the routing and analysis. The application of N-cube networks (i) extend the hypercube principles to any N⩾3 (ii) increase the number of plane host graphs and (iii) reduce the incompleteness of the host cubes. Several different embeddings of the intersection graphs (IGs) of 2-D switching networks and several different routings are explained for N=4 and 6 by various examples. By the expansion of the grids (enlargement) internal waveguides (WGs) and internal switches are introduced which interact with the switches of the original 3-D grid without increasing the number of stages (NS). The embeddings by expansion apply to interconnection networks whereas dilation-2 embeddings (dilation ≡ distance of the nearest-neighbour nodes of the guest graph at the host) are rather suitable for the emulation of algorithms. Concepts for fault-tolerant routing and algorithm mapping are briefly explained.

In this paper, we present a reconfiguration approach to identify the maximal fault-free subcube-ring for tolerating faults in injured hypercubes. The fault-free subcube-ring is connected by a ring of fault-free subcubes with dilation 3. By exploiting the size of fault-free subcubes as large as possible, the maximal fault-free subcube-ring with higher processor utilization is obtained. Using this approach, we can tolerate more than n faults in n-dimensional hypercubes. To demonstrate the fault-tolerant capability of our approach, we implement two fault-tolerant algorithms, matrix-multiplication and sorting algorithms, on the nCUBE/2E hypercube machine with 32 processors. The simulation results show that our reconfiguration approach has low performance slowdown and high processor utilization.

This paper presents a bibliography of nearly 1200 references related to computer vision and image analysis, arranged by subject matter. The topics covered include architectures; computational techniques; feature detection and segmentation; image analysis; two-dimensional shape; pattern; color and texture; matching and stereo; three-dimensional recovery and analysis; three-dimensional shape; and motion. A few references are also given on related topics, such as geometry, graphics, image input/output and coding, image processing, optical processing, visual perception, neural nets, pattern recognition and artificial intelligence, as well as on applications.