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Sloping-and-shaking

Multiway merging and sorting

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Abstract

Most traditional merging and merging-based sorting algorithms are based on 2 sorters or 2 comparators. A new merging technique is developed, namely sloping-and-shaking multiway merging, and a corresponding multiway sorting method based only onk-sorters is proposed. The sloping-and-shaking merging algorithm mergesk sorted lists into one, wherek can be any prime number. The merging process is not a series of recursive applications of 2-way merging. It sorts the keys on them×k plane in vertical and horizontal directions, then along sloping lines with various slope rates step by step. Onlyk-sorters are needed in the merging or sorting process. The time needed to mergek sorted lists, withm of each, is (k+┌log2(m/k)┐)t k, and the time for sortingN keys is (1+(p−1)k+1/2(p−1)(p−2)┌log2 k┐)t k, wherep=log kN, andt k is the time to sortk keys. The proposed algorithms can be implemented either by hardwared sorting networks, or on general purpose parallel and vector machines. The traditional odd-even merging can be viewed as a special case of the multiway merging proposed (whenk is 2). While theoretically the proposed algorithms provide a new understanding of parallel merging and sorting processes, they may be used in practice to construct sorting circuits faster than 2-sorter based sorting methods.

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Authors and Affiliations

  1. University of Science and Technology Beijing, 100083, Beijing, China

    Qingshi Gao

  2. Institute of Computing Technology, Chinese Academy of Sciences, 100080, Beijing, China

    Zhiyong Liu

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  1. Qingshi Gao
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  2. Zhiyong Liu
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Project supported by the National “863” High-Tech Program of China and the National Natural Science Foundation of China.

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Gao, Q., Liu, Z. Sloping-and-shaking. Sci. China Ser. E-Technol. Sci. 40, 225–234 (1997). https://doi.org/10.1007/BF02916597

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  • DOI: https://doi.org/10.1007/BF02916597

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