A logarithmic time sort for linear size networks

A randomized algorithm that sorts on an <italic>N</italic> node network with constant valence in <italic>O</italic>(log <italic>N</italic>) time is given. More particularly, the algorithm sorts <italic>N</italic> items on an <italic>N</italic>-node cube-connected cycles graph, and, for some constant <italic>k</italic>, for all large enough <italic>α</italic>, it terminates within <italic>kα</italic> log <italic>N</italic> time with probability at least 1 - <italic>N</italic><supscrpt>-<italic>α</italic></supscrpt>.

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