## Parallel computation on regular arrays |

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### Contents

Synchronization problems | 27 |

Systematic synthesis of systolic algorithms | 51 |

i | 97 |

Copyright | |

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### Common terms and phrases

adders allocation function application arcs array of figure array of order assigned binary bitonic block boolean cell cellular column comparison-exchanges configuration connected components contains corresponding defined delay denote dependence graph edges firing squad follows functional element Gaussian elimination graph G Hereafter host illustrated in figure implementation Initially input interaction interaction interaction Leiserson lemma length linear array machine matrix product minimum spanning tree node obtained operations optimal timing function pair parallel algorithm parallel computation path PE(j perfect shuffle performed phase pipeline priority queue privileged problem processing elements Proof Proposition queue real-time recurrence equations regular arrays retiming self-stabilizing self-stabilizing system sequence sequential shown in figure shows signed-digit representation SIMD simulation solution sorting sorting networks square factor square matrices steps stored string subarray synchronous system systolic algorithms systolic arrays task allocation method Tchuente Transputer undirected graph unidirectional variables vertex vertices