## Abstract

H. Mannila and E. Ukkonen (1986) have studied a variant of the classical disjoint set union (equivalence) problem in which an extra operation, called de-union, can undo the most recently performed union operation not yet undone. They proposed a way to modify standard set union algorithms to handle de-union operations. In this paper several algorithms are analyzed based on their approach. The most efficient such algorithms have an amortized running time of O(log n/log n) per operation, where n is the total number of elements in all the sets. These algorithms use O(n log n) space, but the space usage can be reduced to O(n) by a simple change. The authors prove that any separable pointer-based algorithm for the problem requires Ω(log n/log log n) time per operation, thus showing that our upper bound on amortized time is tight.

Original language | English (US) |
---|---|

Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | SIAM Journal on Computing |

Volume | 18 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1989 |

## All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Mathematics(all)