Scalable Parallel Geometric Hashing for Hypercube Simd Architectures

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Scalable Parallel Geometric Hashing for Hypercube Simd Architectures
Isidore Rigoutsos
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'■ z" ;/ 1 ' Figure 4. Triple Product: the two stages.
the data along each plane is spread into the entire cube, first spreading the data on the (i, 2/)-plane along the 2-axis, then the data on the (y, z)-plane along the x-axis. And finally the (i, z)-plane along the 2/-axis (see Figure 4). When completed, processor (i, j, k) will have received datum a, from (t, i, 0), datum bj from processor {0, j, k), and datum Ck from processor {i, 0, k) and thus has the triple product element (a, 6j, ct).
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... BUILDING-BLOCK ALGORITHMS 6 The operation of spreading data along a single axis that occurs during both phases can clearly be performed in 0(1, ) time (for the appropriate axis), since nearest neighbors are adjacent in the hypercube, but can in fact be completed in 0(\ogl, ) time. This is because a parallel prefix operation may be used. Namely, the operation is equivalent to a collection of concurrent parallel prefix computations with "copy from the left" as the binary associative operator. The parallel prefix computation makes use of a recursive doubling scheme to spread the data rapidly along the axis.

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