## Abstract

We present the first construction for sorting and counting networks of arbitrary width that requires both small depth and small constant factors in the depth expression. Let ω be the product ω = p_{0} · p_{1} ⋯ p_{n-1}, whose factors are not necessarily prime. We present a novel network construction of width ω and depth O(n^{2}) = O(log^{2} ω), using comparators (or balancers) of width less than or equal to max(P_{i}). This construction is practical in the sense that the asymptotic notation does not hide any large constants. An interesting aspect of this construction is that it establishes a family of sorting and counting networks of width ω, one for each distinct factorization of ω. A factorization in which max(p_{i}) is large and n is small yields a network that trades small depth for large comparators (or balancers), and a factorization where max(p_{i}) is small and n is large makes the opposite tradeoff.

Original language | English (US) |
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Pages (from-to) | 99-128 |

Number of pages | 30 |

Journal | Theory of Computing Systems |

Volume | 35 |

Issue number | 2 |

DOIs | |

State | Published - 2002 |

Externally published | Yes |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics