Networks for sorting multitonic sequences

Lee and Batcher have designed networks that efficiently merge k separately provided sorted sequences of known lengths totalling n. We show that the design is still possible, and in fact easier to describe, if we do not make use of the lengths, or even the directions of monotonicity, of the individual sequences—the sequences can be provided in a single undelimited concatenation of length n. The depth of the simplest resulting network to sort sequences that are “k-tonic” and of length n is , generalizing Batcher's 1968 results for the extreme values of k (k=2 corresponding to merging, and k=n/2 corresponding to general sorting).The exposition is self-contained and can serve even as an introduction to sorting networks and Batcher's results.