## Abstract

We present a set of optimal arid asymptotically optimal sequential and parallel algorithms for the problem of searching on an m x n sorted matrix in the general case when m≤n. Our two sequential algorithms have a time complexity of O(m log(2n/m)) which is shown to be optimal. Our parallel algorithm runs in O(log(log m/log log m) log(2n/m^{1-z})) time using m/log(log m/log log m) processors on a COMMON CRCW PRAM, where 0≤z < 1 is a monotonically decreasing function on m, which is asymptotically work-optimal. The two sequential algorithms differ mainly in the ways of matrix partitioning: one uses row-searching and the other applies diagonal-searching. The parallel algorithm is based on some non-trivial matrix partitioning and processor allocation schemes. All the proposed algorithms can be easily generalized for searching on a set of sorted matrices.

Original language | English |
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Pages (from-to) | 221-230 |

Number of pages | 10 |

Journal | Theoretical Computer Science |

Volume | 188 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 30 Nov 1997 |

Externally published | Yes |

## Keywords

- CRCW PRAM
- Matrix search problem
- Optimal algorithm
- Processors
- Sorted matrix
- Time complexity
- Work-optimal