Periodification scheme

Author:

kutyłowski Mirosław1,Loryś Krzysztof1,Oesterdiekhoff Brigitte2,Wanka Rolf2

Affiliation:

1. Univ. of Wrocław, Wrocław, Poland

2. Paderborn Univ. Paderborn, Germany

Abstract

We consider comparator networks M that are used repeatedly: while the output produced by M is not sorted, it is fed again into M . Sorting algorithms working in this way are called periodic . The number of parallel steps performed during a single run of M is called its period , the sorting time of M is the total number of parallel steps that are necessary to sort in the worst case. Periodic sorting networks have the advantage that they need little hardware (control logic, wiring, area) and that they are adaptive. We are interested in comparator networks of a constant period, due to their potential applications in hardware design. Previously, very little was known on such networks. The fastest solutions required time O(n ε ) where the depth was roughly 1/ε. We introduce a general method called periodification scheme that converts automatically an arbitrary sorting network that sorts n items in time T(n ) and that has layout area A(n ) into a sorting network that has period 5, sorts ***( nT ( n ) items in time O(T(<n )• log n ), and has layout area O(A(n) ) • T(n )). In particular, applying this scheme to Batcher's algorithms, we get practical period 5 comparator networks that sort in time O (log 3 n ). For theoretical interest, one may use the AKS netork resulting in a period 5 comparator network with runtime O (log 2 n ).

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Streaming Sorting Networks;ACM Transactions on Design Automation of Electronic Systems;2016-09-22

2. Faster merging networks with a small constant period;Theoretical Computer Science;2016-08

3. Faster 3-periodic merging networks;Proceedings of the 26th ACM symposium on Parallelism in algorithms and architectures;2014-06-21

4. Networks for sorting multitonic sequences;Journal of Parallel and Distributed Computing;2005-12

5. Fun-Sort—or the chaos of unordered binary search;Discrete Applied Mathematics;2004-12

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