## Improved Algorithms for Finding Level Ancestors in Dynamic Trees (2000)

Venue: | Automata, Languages and Programming, 27th International Colloquium, ICALP 2000, number 1853 in LNCS |

Citations: | 16 - 1 self |

### BibTeX

@INPROCEEDINGS{Alstrup00improvedalgorithms,

author = {Stephen Alstrup and Jacob Holm},

title = {Improved Algorithms for Finding Level Ancestors in Dynamic Trees},

booktitle = {Automata, Languages and Programming, 27th International Colloquium, ICALP 2000, number 1853 in LNCS},

year = {2000},

pages = {73--84},

publisher = {Springer Verlag}

}

### OpenURL

### Abstract

Given a node x at depth d in a rooted tree LevelAncestor(x; i) returns the ancestor to x in depth d i. We show how to maintain a tree under addition of new leaves so that updates and level ancestor queries are being performed in worst case constant time. Given a forest of trees with n nodes where edges can be added, m queries and updates take O(m(m;n)) time. This solves two open problems (P.F.

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Citation Context ... to maintain a forest of trees under insertion and deletion of new edges supporting min queries. Each operation is supported in worst case O(log n) per operation. As trivial applications of top trees =-=[2, 3-=-] LevelAncestor and succ can also be supported in O(log n) worst case time per operation. On a RAM with word size (log n), we have the usual gap to the (log n= log log n) lower bound [12] for fully dy... |

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