## Dynamic Ordered Sets with Exponential Search Trees (2001)

Venue: | Combination of results presented in FOCS 1996, STOC 2000 and SODA |

Citations: | 26 - 1 self |

### BibTeX

@INPROCEEDINGS{Andersson01dynamicordered,

author = {Arne Andersson and Mikkel Thorup},

title = {Dynamic Ordered Sets with Exponential Search Trees},

booktitle = {Combination of results presented in FOCS 1996, STOC 2000 and SODA},

year = {2001}

}

### Years of Citing Articles

### OpenURL

### Abstract

We introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fully-dynamic linear space data structures. This leads to an optimal bound of O ( √ log n/log log n) for searching and updating a dynamic set of n integer keys in linear space. Here searching an integer y means finding the maximum key in the set which is smaller than or equal to y. This problem is equivalent to the standard text book problem of maintaining an ordered set (see, e.g., Cormen, Leiserson, Rivest, and Stein: Introduction to Algorithms, 2nd ed., MIT Press, 2001). The best previous deterministic linear space bound was O(log n/log log n) due Fredman and Willard from STOC 1990. No better deterministic search bound was known using polynomial space.