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External Memory Priority Queues with Decrease-Key and Applications to Graph Algorithms

Authors John Iacono , Riko Jacob, Konstantinos Tsakalidis



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Author Details

John Iacono
  • Department of Computer Science, Université Libre de Bruxelles, Belgium
Riko Jacob
  • Computer Science Department, IT University of Copenhagen, Denmark
Konstantinos Tsakalidis
  • Department of Computer Science, University of Liverpool, United Kingdom

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John Iacono, Riko Jacob, and Konstantinos Tsakalidis. External Memory Priority Queues with Decrease-Key and Applications to Graph Algorithms. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 60:1-60:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ESA.2019.60

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Shortest paths
  • Theory of computation → Data structures design and analysis
  • Hardware → External storage
Keywords
  • priority queues
  • external memory
  • graph algorithms
  • shortest paths
  • depth-first search
  • breadth-first search

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