By Prof. Sanjay Ranka, Prof. Sartaj Sahni (auth.)
Fundamentals algorithms for SIMD and MIMD hypercubes are built. those contain algorithms for such difficulties as info broadcasting, info sum, prefix sum, shift, information movement, info accumulation, sorting, random entry reads and writes and information permutation. the basic algorithms are then used to procure effective hypercube algorithms for matrix multiplication, picture processing difficulties resembling convolution, template matching, hough rework, clustering and snapshot processing transformation, and string enhancing. many of the algorithms during this booklet are for hypercubes with the variety of processors being a functionality of difficulties dimension. even though, for photo processing difficulties, the ebook additionally contains algorithms for and MIMD hypercube with a small variety of tactics. Experimental effects on an NCUBE/77 MIMD hypercube also are awarded. The booklet is acceptable to be used in a one-semester or one-quarter path on hypercube algorithms. for college kids without previous publicity to parallel algorithms, it is suggested that one week might be spent at the fabric in bankruptcy 1, approximately six weeks on bankruptcy 2 and one week on bankruptcy three. the rest of the time period might be spent masking issues from the remainder of the book.
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Extra resources for Hypercube Algorithms: with Applications to Image Processing and Pattern Recognition
The objective is to move the ranked records in each window to the processor whose position in the window equals the record rank. 11 gives an initial configuration for an SIMD eight processor window. The records are shown as pairs with the second entry in each pair being the rank. We assume that the processors that are not selected for the concentration operation have a rank of 00. The result of the concentration is shown in line 1. 11 Example to concentrate in an SIMD hypercube Data concentration can be done in O(k) time by obtaining agreement between the bits of the destination of a record and its present location in the order 0, 1, 2, ...
13. When i is a power of 2 (l>HighBit), a data transfer along bit I = f (lOg2M, i) is to be performed. This will be followed by a circulation in subhypercubes of size i (circulation in a subhypercube of size 1 is null). The data required by each subhypercube depends on the l'th bit of the PEs in that subhypercube (all PEs in the subhypercube have the same l'th bit). If this bit is zero, data is coming from a right adjacent subhypercube with l'th bit equal to 1. So, PEs with this bit being 1 should transmit their lold values.
The 8 processors may be partitioned into two windows of size 4 each. The left window consists of processors 0 through 3 and processors 4 through 7 make up the right window. 5. SHIFT 33 and d are initially in the left window and they are in the right window after the shift. Also, f, g, and h are initially in the right window and are in the left window following the shift. If we exchange b, c, and d with f, g, and h, respectively, then we obtain the configuration of line 3. Now each of the two windows of size 4 has the data it needs for its final configuration.