K-bitonic sort

Abstract

Ak-bitonic sort which generalizes the bitonic sort is proposed. The theorem of the bitonic sort, which merges two monotonic sequences into one order sequence, is extended into the theorem ofk-bitonic sort. Thek-bitonic sort merges (K (=2k or 2k−1) monotonic sequences into one order sequence in\(\left\lceil {log_2 K} \right\rceil \left\lceil {log_2 N} \right\rceil - \tfrac{{\left\lceil {log_2 K} \right\rceil (\left\lceil {log_2 K} \right\rceil - 1)}}{2}\) steps, where\(k = \left\lceil {\tfrac{K}{2}} \right\rceil \) is an integer andk≥1. Thek-bitonic sort is the Batcher's bitonic sort whenk=1.