Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Iacono, John; Jacob, Riko; Tsakalidis, Konstantinos http://www.dagstuhl.de/lipics License
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URN: urn:nbn:de:0030-drops-111817
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External Memory Priority Queues with Decrease-Key and Applications to Graph Algorithms

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Abstract

We present priority queues in the external memory model with block size B and main memory size M that support on N elements, operation Update (a combination of operations Insert and DecreaseKey) in O(1/Blog_{M/B} N/B) amortized I/Os and operations ExtractMin and Delete in O(ceil[(M^epsilon)/B log_{M/B} N/B] log_{M/B} N/B) amortized I/Os, for any real epsilon in (0,1), using O(N/Blog_{M/B} N/B) blocks. Previous I/O-efficient priority queues either support these operations in O(1/Blog_2 N/B) amortized I/Os [Kumar and Schwabe, SPDP '96] or support only operations Insert, Delete and ExtractMin in optimal O(1/Blog_{M/B} N/B) amortized I/Os, however without supporting DecreaseKey [Fadel et al., TCS '99]. We also present buffered repository trees that support on a multi-set of N elements, operation Insert in O(1/Blog_M/B N/B) I/Os and operation Extract on K extracted elements in O(M^{epsilon} log_M/B N/B + K/B) amortized I/Os, using O(N/B) blocks. Previous results achieve O(1/Blog_2 N/B) I/Os and O(log_2 N/B + K/B) I/Os, respectively [Buchsbaum et al., SODA '00]. Our results imply improved O(E/Blog_{M/B} E/B) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed dense graphs (V,E) with E = Omega (V^(1+epsilon)), epsilon > 0 and V = Omega (M), which is equal to the I/O-optimal bound for sorting E values in external memory.

BibTeX - Entry

@InProceedings{iacono_et_al:LIPIcs:2019:11181,
  author =	{John Iacono and Riko Jacob and Konstantinos Tsakalidis},
  title =	{{External Memory Priority Queues with Decrease-Key and Applications to Graph Algorithms}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{60:1--60:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Michael A. Bender and Ola Svensson and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11181},
  URN =		{urn:nbn:de:0030-drops-111817},
  doi =		{10.4230/LIPIcs.ESA.2019.60},
  annote =	{Keywords: priority queues, external memory, graph algorithms, shortest paths, depth-first search, breadth-first search}
}

Keywords: priority queues, external memory, graph algorithms, shortest paths, depth-first search, breadth-first search
Seminar: 27th Annual European Symposium on Algorithms (ESA 2019)
Issue date: 2019
Date of publication: 2019


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