Showing papers on "Quantum sort published in 1989"

Parallel sorting in two-dimensional VLSI models of computation

Abstract: The gradual refinement of a general approach to two-dimensional sorting, the shear-sort algorithm, to more sophisticated and specialized sorting algorithms on mesh-connected computers is described. The analysis of the shear-sort algorithm gives rise to a novel perspective of two-dimensional sorting, which seems to be a very powerful tool for developing efficient algorithms. The same methods can be extended for sorting in higher dimensions, for example, in the three-dimensional mesh. The concept of clean and dirty rows can be modified to clean and dirty planes (or hyperplanes for dimensions greater than three). Although only two schemes (purely recursive and iterative) are explicitly described, the reader may construct his own algorithm using similar technique and slight modifications. Designing an O(n) algorithm for sorting on a mesh becomes much simpler using the techniques developed. >

Efficient communication in massively parallel computers

Abstract: A fundamental operation in parallel computation is sorting. Sorting is important not only because it is required by many algorithms, but also because it can be used to implement irregular, pointer-based communication. We study two algorithms for sorting in massively parallel computers. First, we examine Shellsort. Shellsort is a sorting algorithm that is based on a sequence of parameters called increments. Shellsort can be used to create a parallel sorting device known as a sorting network. Researchers have suggested that if the correct increment sequence is used, an optimal size sorting network can be obtained. All published increment sequences have been monotonically decreasing. We show that no monotonically decreasing increment sequence will yield an optimal size sorting network. Second, we present a sorting algorithm called Cubesort. Cubesort is the fastest known sorting algorithm for a variety of parallel computers over a wide range of parameters. We also present a paradigm for developing parallel algorithms that have efficient communication. The paradigm, called the data reduction paradigm, consists of using a divide-and-conquer strategy. Both the division and combination phases of the divide-and-conquer algorithm may require irregular, pointer-based communication between processors. However, the problem is divided so as to limit the amount of data that must be communicated. As a result the communication can be performed efficiently. We present data reduction algorithms for the image component labeling problem, the closest pair problem and four versions of the parallel prefix problem.