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All-pairs nearly 2-approximate shortest-paths in O(n² polylog n) time (2005)
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| Venue: | IN PROCEEDINGS OF 22ND ANNUAL SYMPOSIUM ON THEORETICAL ASPECT OF COMPUTER SCIENCE, VOLUME 3404 OF LNCS |
| Citations: | 13 - 6 self |
BibTeX
@INPROCEEDINGS{Baswana05all-pairsnearly,
author = {Surender Baswana and Vishrut Goyal and Sandeep Sen},
title = {All-pairs nearly 2-approximate shortest-paths in O(n² polylog n) time},
booktitle = {IN PROCEEDINGS OF 22ND ANNUAL SYMPOSIUM ON THEORETICAL ASPECT OF COMPUTER SCIENCE, VOLUME 3404 OF LNCS},
year = {2005},
pages = {666--679},
publisher = {Springer}
}
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Abstract
Let G(V, E) be an unweighted undirected graph on |V| = n vertices. Let δ(u, v) denote the shortest distance between vertices u, v ∈ V. An algorithm is said to compute all-pairs t-approximate shortest-paths/distances, for some t ≥ 1, if for each pair of vertices u, v ∈ V, the path/distance reported by the algorithm is not longer/greater than t · δ(u, v). This paper presents two randomized algorithms for computing all-pairs nearly 2-approximate distances. The first algorithm takes expected O(m 2/3 n log n+n²) time, and for any u, v ∈ V reports distance no greater than 2δ(u, v) + 1. Our second algorithm requires expected O(n² log 3/2) time, and for any u, v ∈ V reports distance bounded by 2δ(u, v) + 3. This paper also presents the first expected O(n 2) time algorithm to compute all-pairs 3-approximate distances.
