Fully dynamic algorithms for chordal graphs (1999)
| Venue: | In Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'99 |
| Citations: | 26 - 1 self |
BibTeX
@INPROCEEDINGS{Ibarra99fullydynamic,
author = {Louis Ibarra},
title = {Fully dynamic algorithms for chordal graphs},
booktitle = {In Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'99},
year = {1999},
pages = {923--924}
}
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Abstract
We present the rst dynamic algorithm that maintains a clique tree representation of a chordal graph and supports the following operations: (1) query whether deleting or inserting an arbitrary edge preserves chordality, (2) delete or insert an arbitrary edge, provided it preserves chordality. Wegivetwo implementations. In the rst, each operation runs in O(n) time, where n is the numberofvertices. In the second, an insertion query runs in O(log 2 n) time, an insertion in O(n) time, a deletion query in O(n) time, and a deletion in O(n log n) time. We also present a data structure that allows a deletion query to run in O ( p m) time in either implementation, where m is the current number of edges. Updating this data structure after a deletion or insertion requires O(m) time. We also present avery simple dynamic algorithm that supports each of the following operations in O(1) time on a general graph: (1) query whether the graph is split, (2) delete or insert an arbitrary edge. 1
