### Abstract

Hypercubic 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 hypercubic 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 hypercubic 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 hypercubic sorting network. Our lower bound can be extended to certain restricted classes of non-oblivious sorting algorithms on hypercubic machines.

Original language | English (US) |
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Title of host publication | Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings |

Publisher | Springer Verlag |

Pages | 618-629 |

Number of pages | 12 |

Volume | 820 LNCS |

ISBN (Print) | 9783540582014 |

State | Published - 1994 |

Event | Proceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94 - Jerusalem, Isr Duration: Jul 1 1994 → Jul 1 1994 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 820 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | Proceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94 |
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City | Jerusalem, Isr |

Period | 7/1/94 → 7/1/94 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings*(Vol. 820 LNCS, pp. 618-629). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 820 LNCS). Springer Verlag.

**A super-logarithmic lower bound for hypercubic sorting networks.** / Plaxton, C. Greg; Suel, Torsten.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings.*vol. 820 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 820 LNCS, Springer Verlag, pp. 618-629, Proceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94, Jerusalem, Isr, 7/1/94.

}

TY - GEN

T1 - A super-logarithmic lower bound for hypercubic sorting networks

AU - Plaxton, C. Greg

AU - Suel, Torsten

PY - 1994

Y1 - 1994

N2 - Hypercubic 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 hypercubic sorting networks with depth 2O(√lg lg n) lg n have been discovered. These networks are the only known sorting networks of depth o(lg2n) 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 hypercubic 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 hypercubic sorting network. Our lower bound can be extended to certain restricted classes of non-oblivious sorting algorithms on hypercubic machines.

AB - Hypercubic 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 hypercubic sorting networks with depth 2O(√lg lg n) lg n have been discovered. These networks are the only known sorting networks of depth o(lg2n) 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 hypercubic 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 hypercubic sorting network. Our lower bound can be extended to certain restricted classes of non-oblivious sorting algorithms on hypercubic machines.

UR - http://www.scopus.com/inward/record.url?scp=0040347774&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040347774&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783540582014

VL - 820 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 618

EP - 629

BT - Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings

PB - Springer Verlag

ER -