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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2016.13
URN: urn:nbn:de:0030-drops-63640
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6364/
Bilo, Davide ;
Guala, Luciano ;
Leucci, Stefano ;
Proietti, Guido
Compact and Fast Sensitivity Oracles for Single-Source Distances
Abstract
Let s denote a distinguished source vertex of a non-negatively real weighted and undirected graph G with n vertices and m edges. In this paper we present two efficient single-source approximate-distance sensitivity oracles, namely compact data structures which are able to quickly report an approximate (by a multiplicative stretch factor) distance from s to any node of G following the failure of any edge in G. More precisely, we first present a sensitivity oracle of size O(n) which is able to report 2-approximate distances from the source in O(1) time. Then, we further develop our construction by building, for any 0<epsilon<1, another sensitivity oracle having size O(n*1/epsilon*log(1/epsilon)), and is able to report a (1+epsilon)-approximate distance from s to any vertex of G in O(log(n)*1/epsilon*log(1/epsilon)) time. Thus, this latter oracle is essentially optimal as far as size and stretch are concerned, and it only asks for a logarithmic query time. Finally, our results are complemented with a space lower bound for the related class of single-source additively-stretched sensitivity oracles, which is helpful to realize the hardness of designing compact oracles of this type.
BibTeX - Entry
@InProceedings{bilo_et_al:LIPIcs:2016:6364,
author = {Davide Bilo and Luciano Guala and Stefano Leucci and Guido Proietti},
title = {{Compact and Fast Sensitivity Oracles for Single-Source Distances}},
booktitle = {24th Annual European Symposium on Algorithms (ESA 2016)},
pages = {13:1--13:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-015-6},
ISSN = {1868-8969},
year = {2016},
volume = {57},
editor = {Piotr Sankowski and Christos Zaroliagis},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6364},
URN = {urn:nbn:de:0030-drops-63640},
doi = {10.4230/LIPIcs.ESA.2016.13},
annote = {Keywords: fault-tolerant shortest-path tree, approximate distance, distance sensitivity oracle}
}
Keywords: |
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fault-tolerant shortest-path tree, approximate distance, distance sensitivity oracle |
Collection: |
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24th Annual European Symposium on Algorithms (ESA 2016) |
Issue Date: |
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2016 |
Date of publication: |
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18.08.2016 |