License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2018.72
URN: urn:nbn:de:0030-drops-90766
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9076/
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Gupta, Manoj ; Singh, Aditi

Generic Single Edge Fault Tolerant Exact Distance Oracle

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LIPIcs-ICALP-2018-72.pdf (0.5 MB)


Abstract

Given an undirected unweighted graph G and a source set S of |S| = sigma sources, we want to build a data structure which can process the following query Q(s,t,e): find the shortest distance from s to t avoiding an edge e, where s in S and t in V. When sigma=n, Demetrescu, Thorup, Chowdhury and Ramachandran (SIAM Journal of Computing, 2008) designed an algorithm with O~(n^2) space and O(1) query time. A natural open question is to generalize this result to any number of sources. Recently, Bil{ò} et. al. (STACS 2018) designed a data-structure of size O~(sigma^{1/2}n^{3/2}) with the query time of O(sqrt{n sigma}) for the above problem. We improve their result by designing a data-structure of size O~(sigma^{1/2} n^{3/2}) that can answer queries in O~(1) time. In a related problem of finding fault tolerant subgraph, Parter and Peleg (ESA 2013) showed that if detours of replacement paths ending at a vertex t are disjoint, then the number of such paths is O(sqrt{n sigma}). This eventually gives a bound of O(n sqrt{n sigma}) = O(sigma^{1/2}n^{3/2}) for their problem. Disjointness of detours is a very crucial property used in the above result. We show a similar result for a subset of replacement path which may not be disjoint. This result is the crux of our paper and may be of independent interest.

BibTeX - Entry

@InProceedings{gupta_et_al:LIPIcs:2018:9076,
  author =	{Manoj Gupta and Aditi Singh},
  title =	{{Generic Single Edge Fault Tolerant Exact Distance Oracle}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{72:1--72:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9076},
  URN =		{urn:nbn:de:0030-drops-90766},
  doi =		{10.4230/LIPIcs.ICALP.2018.72},
  annote =	{Keywords: Fault Tolerant Algorithms, Graph Algorithms, Distance Oracles, Data-Structures}
}

Keywords: Fault Tolerant Algorithms, Graph Algorithms, Distance Oracles, Data-Structures
Collection: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 04.07.2018


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