## A Fully Dynamic Algorithm for Maintaining the Transitive Closure (1999)

Venue: | In Proc. 31st ACM Symposium on Theory of Computing (STOC'99 |

Citations: | 43 - 1 self |

### BibTeX

@INPROCEEDINGS{King99afully,

author = {Valerie King and Garry Sagert},

title = {A Fully Dynamic Algorithm for Maintaining the Transitive Closure},

booktitle = {In Proc. 31st ACM Symposium on Theory of Computing (STOC'99},

year = {1999},

pages = {492--498},

publisher = {ACM}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper presents an efficient fully dynamic graph algorithm for maintaining the transitive closure of a directed graph. The algorithm updates the adjacency matrix of the transitive closure with each update to the graph. Hence, each reachability query of the form "Is there a directed path from i to j?" can be answered in O(1) time. The algorithm is randomized; it is correct when answering yes, but has O(1/n^c) probability of error when answering no, for any constant c. In acyclic graphs, worst case update time is O(n^2). In general graphs, update time is O(n^(2+alpha)), where alpha = min {.26, maximum size of a strongly connected component}. The space complexity of the algorithm is O(n^2).

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Citation Context ...th cost O(m \Delta) for m deletions, where m is the number of edges in the transitive closure and \Delta is the out-degree of the initial graph . There is a Monte Carlo algorithm of E. Cohen's (1997) =-=[1]-=- for computing static transitive closure (i.e. transitive closure from scratch) based on her linear time algorithm for estimating the size of the transitive closure. However, this algorithm has O(mn) ... |

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