## Parallel Computation on Regular Arrays |

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### Contents

vi | 26 |

Synchronization problems | 27 |

Summary and bibliographic notes | 48 |

Summary and bibliographic notes | 94 |

Parallel adders | 111 |

Sorting | 127 |

Matrix product | 161 |

Linear system solvers | 209 |

Summary and bibliographic notes | 234 |

viii | 275 |

298 | |

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### Common terms and phrases

adders allocation function arcs array of figure array of order assigned binary bitonic block boolean cell cellular coefficients column computation date connected components contains corresponding cycle defined delay denote dependence graph edges follows functional element Gaussian elimination graph G Hereafter host illustrated in figure implementation induction integer interaction interaction lag(u leftmost Leiserson lemma linear array Machine PE(0 matrix product minimum spanning tree moves neighbours node obtained operations optimal timing function output pair parallel algorithm parallel computation path PE(i PE(j PE(n perfect shuffle performed phase pipeline priority queue privileged processing elements Proof Proposition real-time recurrence equations regular arrays retiming segment self-stabilizing system shown in figure shows signal signed-digit representation SIMD simulation SISYC solution sorting sorting networks steps stored string subarray subnetwork synchronous system systolic algorithms systolic arrays task allocation method Tchuente transforms Transputer undirected undirected graph variables vertex vertices