## Abstract

Shuffle-unshuffle sorting networks are a class of comparator networks whose structure maps efficiently to the hypercube and any of its bounded degree variants. Recently, n-input shuffle-unshuffle sorting networks with depth 2^{O(√lg lg n)} lg n have been discovered. These networks are the only known sorting networks of depth o(lg^{2} n) that are not based on expanders, and their existence raises the question of whether a depth of O (lg n) can be achieved by any shuffle-unshuffle sorting network. In this paper we resolve this question by establishing an Ω (lg n lg lg n/lg lg lg n) lower bound on the depth of any n-input shuffle-unshuffle sorting network. Our lower bound can be extended to certain restricted classes of nonoblivious sorting algorithms on hypercubic machines.

Original language | English (US) |
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Pages (from-to) | 233-254 |

Number of pages | 22 |

Journal | Theory of Computing Systems |

Volume | 33 |

Issue number | 3 |

DOIs | |

State | Published - 2000 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics