## Abstract

Given an array of n input numbers, the range-maxima problem is that of preprocessing the data so that queries of the type "what is the maximum value in subarray [i..j]" can be answered quickly using one processor. We present a randomized preprocessing algorithm that runs in O(log^{*}n) time with high probability, using an optimal number of processors on a CRCW PRAM; each query can be processed in constant time by one processor. We also present a randomized algorithm for a parallel comparison model. Using an optimal number of processors, the preprocessing algorithm runs in O(α (n)) time with high probability; each query can be processed in O (α (n)) time by one processor. (As is standard, α(n) is the inverse of Ackermann function.) A constant time query can be achieved by some slowdown in the performance of the preprocessing stage.

Original language | English |
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Pages (from-to) | 350-373 |

Number of pages | 24 |

Journal | Computational Complexity |

Volume | 2 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1992 |

## Keywords

- PRAM
- Subject classifications: 68Q20
- comparison model
- parallel algorithms
- prefix maximum
- randomized algorithms
- range maximum