By Quentin F. Miller Russ;Stout
Parallel-Algorithms for normal Architectures is the 1st ebook to pay attention solely on algorithms and paradigms for programming parallel pcs similar to the hypercube, mesh, pyramid, and mesh-of-trees. Algorithms are given to unravel primary projects equivalent to sorting and matrix operations, in addition to difficulties within the box of snapshot processing, graph thought, and computational geometry. the 1st bankruptcy defines the pc types, difficulties to be solved, and notation that may be used in the course of the publication. It additionally describes basic summary facts circulation operations that function the root to the various algorithms offered within the publication. the remainder chapters describe effective implementations of those operations for particular types of computation and current algorithms (with asymptotic analyses) which are frequently according to those operations.
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Parallel-Algorithms for normal Architectures is the 1st ebook to pay attention solely on algorithms and paradigms for programming parallel desktops equivalent to the hypercube, mesh, pyramid, and mesh-of-trees. Algorithms are given to unravel primary projects corresponding to sorting and matrix operations, in addition to difficulties within the box of snapshot processing, graph thought, and computational geometry.
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Extra info for Parallel algorithms for regular architectures: meshes and pyramids
The solution to this problem can be obtained in Θ(n) time by a series of row and column rotations, as follows. ) 1. Perform a row rotation so that every processor Pi in row j knows aj*n ⊗ aj*n+1 ⊗ ⋅ ⋅ ⋅ ai. 2. Perform a row rotation so that processor Pj *n,0 ≤ j ≤ n - 1, knows the value stored in processor P[(j+1)*n]1 , namely, aj*n ⊗ aj*n+ 1 ⊗ · · · a[(j+1)*n]-1. 3. Perform a column rotation in column 0 so that processor Pj *n,1 ≤ j ≤ n - 1, knows Vj = a0 ⊗ al ⊗ ⋅ ⋅ ⋅ ⊗ aj*n-1. 4. Perform a row rotation in every row j, 0 ≤ j ≤ n - 1, to broadcast Vj to all processors in row j so they may update their value to obtain a0 ⊗ a1 ⊗ · · · ⊗ ai, for every processor Pi, 0 ≤ i ≤ n2 - 1.
Notice that at any step, a processor has copies of (and views) at most two sets of data. The algorithm terminates the step before processors would simultaneously receive copies of their original data from their western (southern) neighbor. This rotation takes exactly 2n - 3 steps. 2 Passing a Row (Column) Through the Mesh Suppose that every processor of a mesh of size n2 needs to view a fixed amount of data from every processor of a given row (column). This can be done in Θ(n) time as follows. Rotate all columns (rows) simultaneously so that a copy of (the required data from) the given row (column) exists in every row (column) of the mesh.
11 represents the labels of figures after the independent and parallel recursive labeling of the quadrants, then figures A and H are labeled correctly, while the other figures contain pixels with an incorrect final label. Two methods for resolving the labeling conflicts to obtain correct global labels from the local (quadrant) labels are given. Both algorithms exploit the fact that the pertinent data has been reduced from an amount proportional to the area of the image to an amount proportional to the perimeter of the image.
Parallel algorithms for regular architectures: meshes and pyramids by Quentin F. Miller Russ;Stout