### 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 |

State | Published - May 2000 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Mathematics(all)

### Cite this

*Theory of Computing Systems*,

*33*(3), 233-254.

**A superlogarithmic lower bound for shuffle-unshuffle sorting networks.** / Plaxton, C. G.; Suel, T.

Research output: Contribution to journal › Article

*Theory of Computing Systems*, vol. 33, no. 3, pp. 233-254.

}

TY - JOUR

T1 - A superlogarithmic lower bound for shuffle-unshuffle sorting networks

AU - Plaxton, C. G.

AU - Suel, T.

PY - 2000/5

Y1 - 2000/5

N2 - 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 2O(√lg lg n) lg n have been discovered. These networks are the only known sorting networks of depth o(lg2 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.

AB - 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 2O(√lg lg n) lg n have been discovered. These networks are the only known sorting networks of depth o(lg2 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.

UR - http://www.scopus.com/inward/record.url?scp=0034423749&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034423749&partnerID=8YFLogxK

M3 - Article

VL - 33

SP - 233

EP - 254

JO - Theory of Computing Systems

JF - Theory of Computing Systems

SN - 1432-4350

IS - 3

ER -