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DOI: 10.4230/LIPIcs.ESA.2016.28

Optimal Reachability and a Space-Time Tradeoff for Distance Queries in Constant-Treewidth Graphs

Authors: Krishnendu Chatterjee, Rasmus Rasmus Ibsen-Jensen, and Andreas Pavlogiannis

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract

We consider data-structures for answering reachability and distance queries on constant-treewidth graphs with n nodes, on the standard RAM computational model with wordsize W=Theta(log n). Our first contribution is a data-structure that after O(n) preprocessing time, allows (1) pair reachability queries in O(1) time; and (2) single-source reachability queries in O(n/log n) time. This is (asymptotically) optimal and is faster than DFS/BFS when answering more than a constant number of single-source queries. The data-structure uses at all times O(n) space. Our second contribution is a space-time tradeoff data-structure for distance queries. For any epsilon in [1/2,1], we provide a data-structure with polynomial preprocessing time that allows pair queries in O(n^{1-\epsilon} alpha(n)) time, where alpha is the inverse of the Ackermann function, and at all times uses O(n^epsilon) space. The input graph G is not considered in the space complexity.

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Krishnendu Chatterjee, Rasmus Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. Optimal Reachability and a Space-Time Tradeoff for Distance Queries in Constant-Treewidth Graphs. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 28:1-28:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chatterjee_et_al:LIPIcs.ESA.2016.28,
  author =	{Chatterjee, Krishnendu and Rasmus Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
  title =	{{Optimal Reachability and a Space-Time Tradeoff for Distance Queries in Constant-Treewidth Graphs}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{28:1--28:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.28},
  URN =		{urn:nbn:de:0030-drops-63797},
  doi =		{10.4230/LIPIcs.ESA.2016.28},
  annote =	{Keywords: Graph algorithms, Constant-treewidth graphs, Reachability queries, Distance queries}
}

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Documents authored by Rasmus Ibsen-Jensen, Rasmus

Optimal Reachability and a Space-Time Tradeoff for Distance Queries in Constant-Treewidth Graphs

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