# Off-Line Lowest Common Ancestor (Lowest Common Ancestor)

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## Description

Given a collection of rooted trees, answer queries of the form, "What is the nearest common ancestor of vertices $x$ and $y$?" In this version of the problem, the collection of trees is static and the entire sequence of queries is specified in advance.

## Related Problems

Generalizations: Lowest Common Ancestor

Related: Lowest Common Ancestor with Static Trees, Lowest Common Ancestor with Linking Roots, Lowest Common Ancestor with Linking, Lowest Common Ancestors with Linking and Cutting

## Parameters

$n$: number of vertices

$m$: number of total number of operations (queries, links, and cuts)

## Table of Algorithms

Name | Year | Time | Space | Approximation Factor | Model | Reference |
---|---|---|---|---|---|---|

Tarjan's off-line lowest common ancestors algorithm | 1984 | $O(n+m)$ | $O(n)$ | Exact | Deterministic | Time & Space |

Aho, Hopcroft, and Ullman (Offline) | 1976 | $O(n+ m*alpha(m + n, n)$) where alpha is the inverse Ackermann function | $O(n)$ | Exact | Deterministic | Time & Space |