NDLI: Sequential Permutation Networks

Content Provider	IEEE Xplore Digital Library
Author	Harada, K.
Copyright Year	1968
Abstract	Two sequential permutation networks which generate all nǃ permutations without duplication are presented. Each permutation can be derived from its predecessor autonomously in one clock step. Based on the principle of recursive execution of a product of transpositions, the first network is constructed in multiple cascades of ½(n^²-n) switching elements each of which permutes its input pair to its output pair according to its internal state, and is controlled sequentially by the same principle. Next, the network whose structure and control sequence are complementary to those of the first is presented. The first is named a cyclic permutation network and is an explicit representation of a mapping function The second is named a lexicographic permutation network and is an explicit representation of a factorial counting function where ah is a h-nary factorial digit 0 ≤ ah ≤ (n-1). The characteristics of the networks are investigated by establishing a one-to-one correspondence among nI integers, n! permutations, and n! states of the networks. For the lexicographic permutation network which can generate all permutations in lexicographic order, three examples of applications are given.
Sponsorship	IEEE Computer Society Technical Committee on Distributed Process IEEE Computer Society Technical Committee on VLSI IEEE Technical Committee on Computer Architecture IEEE Computer Society
Starting Page	472
Ending Page	479
Page Count	8
File Size	1496709
File Format	PDF
ISSN	00189340
Volume Number	C-21
Issue Number	5
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1972-05-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Combinatorial algebra, permutation networks, sequential circuits, special-purpose digital circuits, switching networks.
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Software Hardware and Architecture

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