Worst-Case Efficient External-Memory Priority Queues

Gerth Stølting Brodal and Jyrki Katajainen

Technical Report, DIKU Report 97/25, Department of Computer Science, University of Copenhagen, 16 pages, October 1997.


A priority queue Q is a data structure that maintains a collection of elements, each element having an associated priority drawn from a totally ordered universe, under the operations Insert, which inserts an element into Q, and DeleteMin, which deletes an element with the minimum priority from Q. In this paper a priority-queue implementation is given which is efficient with respect to the number of block transfers or I/Os performed between the internal and external memories of a computer. Let B and M denote the respective capacity of a block and the internal memory measured in elements. The developed data structure handles any intermixed sequence of Insert and DeleteMin operations such that in every disjoint interval of B consecutive priority-queue operations at most c logM/B (N/M) I/Os are performed, for some positive constant c. These I/Os are divided evenly among the operations: if Bc logM/B (N/M), one I/O is necessary for every B/(clogM/B (N/M))th operation and if B < c logM/B (N/M), c/BĚlogM/B (N/M) I/Os are performed per every operation. Moreover, every operation requires O(log2 N) comparisons in the worst case. The best earlier solutions can only handle a sequence of S operations with O(sumi=1S (1/B)logM/B (Ni/M)) I/Os, where Ni denotes the number of elements stored in the data structure prior to the ith operation, without giving any guarantee for the performance of the individual operations.

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BIBTEX entry

  author = "Gerth St{\o}lting Brodal and Jyrki Katajainen",
  institution = "Department of Computer Science, University of Copenhagen",
  month = "October",
  number = "DIKU Report 97/25",
  pages = "16",
  title = "Worst-Case Efficient External-Memory Priority Queues",
  year = "1997"