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Approximate distance oracles for unweighted graphs . . .
| Citations: | 53 - 10 self |
BibTeX
@MISC{Baswana_approximatedistance,
author = {Surender Baswana and Sandeep Sen},
title = {Approximate distance oracles for unweighted graphs . . .},
year = {}
}
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Abstract
������������ � Let be an undirected graph � on vertices, and ���������� � let denote the distance � in between two � vertices � and. Thorup and Zwick showed that for any +ve � integer, the � graph can be preprocessed to build a data-structure that can efficiently � report-approximate distance between any pair of vertices. That is, for �������� � any, the distance � ���������� � reported satisfies The remarkable feature of this data-structure is that, ���� � for, it occupies sub-quadratic space, i.e., it does not store all-pairs distances information explicitly, and still it can answer � any-approximate distance query in constant time. They named the data-structure “oracle ” because of this feature. Furthermore the tradeoff between � stretch and the size of the data-structure is essentially optimal. In this paper we show that we can actually construct approximate distance oracles in ��������� expected time if the graph is unweighted. One of the new ideas used in the improved algorithm also leads to the first linear time algorithm for computing an optimal �������� � size-spanner of an unweighted graph.
