### Abstract

The authors consider the following problem: Given a collection of rooted trees, answer on-line queries of the form, 'What is the nearest common ancestor of vertices x and y? ' They show that any pointer machine that solves this problem requires OMEGA (log log n) time per query in the worst case, where n is the total number of vertices in the trees. On the other hand, they present an algorithm for a random access machine with uniform cost measure (and a bound of O(log n) on the number of bits per word) that requires O(1) time per query and O(n) preprocessing time, assuming that the collection of trees is static. For a version of the problem in which the trees can change between queries, they obtain an almost-linear-time (and linear-space) algorithm.

Original language | English (US) |
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Pages (from-to) | 338-355 |

Number of pages | 18 |

Journal | SIAM Journal on Computing |

Volume | 13 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1984 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Mathematics(all)

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## Cite this

*SIAM Journal on Computing*,

*13*(2), 338-355. https://doi.org/10.1137/0213024