# lca: O(log n) persistent on-line lowest common ancestor calculation without preprocessing

Versions | 0.1, 0.1.0.1, 0.2, 0.2.1, 0.2.2, 0.2.3, 0.2.4, 0.3, 0.3.1 |
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Change log | CHANGELOG.md |

Dependencies | base (>=4 && <4.8) [details] |

License | BSD-3-Clause |

Copyright | Copyright (C) 2011-2012 Edward A. Kmett |

Author | Edward A. Kmett |

Maintainer | Edward A. Kmett <ekmett@gmail.com> |

Revised | Revision 1 made by HerbertValerioRiedel at Thu Jun 1 09:09:54 UTC 2017 |

Category | Algorithms, Data Structures |

Home page | http://github.com/ekmett/lca/ |

Bug tracker | http://github.com/ekmett/lca/issues |

Source repo | head: git clone git://github.com/ekmett/lca.git |

Uploaded | by EdwardKmett at Wed May 8 23:02:13 UTC 2013 |

Distributions | LTSHaskell:0.3.1, NixOS:0.3.1, Stackage:0.3.1, openSUSE:0.3.1 |

Downloads | 3936 total (30 in the last 30 days) |

Rating | 2.0 (votes: 1) [estimated by rule of succession] |

Your Rating | |

Status | Docs uploaded by user Build status unknown [no reports yet] Hackage Matrix CI |

This package provides a reference implementation of my skew binary random access algorithm for performing an *online* lowest common ancestor search (and online level ancestor search) in logarithmic time without preprocessing. This improves the previous known asymptotic bound for both of these problems from *O(h)* to *O(log h)*, where *h* is the height of the tree. Mostly importantly this bound is completely independent of the width or overall size of the tree, enabling you to calculate lowest common ancestors in a distributed fashion with good locality.

While *offline* algorithms exist for both of these algorithms that that provide *O(1)* query time, they all require at least *O(n)* preprocessing, where *n* is the size of the entire tree, and so are less suitable for LCA search in areas such as revision control where the tree is constantly updated, or distributed computing where the tree may be too large to fit in any one computer's memory.

Slides are available from

http://www.slideshare.net/ekmett/skewbinary-online-lowest-common-ancestor-search

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## Downloads

- lca-0.2.3.tar.gz [browse] (Cabal source package)
- Package description (revised from the package)

Note: This package has metadata revisions in the cabal description newer than included in the tarball. To unpack the package including the revisions, use 'cabal get'.