A Hypercubic Sorting Network with Nearly Logarithmic Depth

A natural class of "hypercubic" sorting networks is defined. The regular structure of these sorting networks allows for elegant and efficient implementations on any of the so-called hypercubic networks (e.g., the hypercube, shuffle-exchange, butterfly, and cube-connected cycles). This class of sorting networks contains Batcher's O(lg 2 n)-depth bitonic sort, but not the O(lg n)-depth sorting network of Ajtai, Koml'os, and Szemer'edi. In fact, no o(lg 2 n)- depth compare-interchange sort was previously known for any of the hypercubic networks. In this paper, we prove the existence of a family of 2 O( p lg lg n) lg n-depth hypercubic sorting networks. Note that this depth is o(lg 1+ffl n) for any constant ffl ? 0. 1 Introduction A comparator network is an n-input, n-output acyclic circuit made up of wires and 2-input, 2output comparator gates. The input wires of the network are numbered from 0 to n \Gamma 1, as are the output wires. The inputs to the network may be tho..

Small-depth counting networks and related topics

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994.Includes bibliographical references (p. 89-92).by Michael Richard Klugerman.Ph.D

Computers, 29:213-222, 1980.

[12] C. G. Plaxton. A hypercubic sorting network with nearly logarithmic depth. In Pro

Sorting networks using k-comparators

Bibliography: leaves 160-167