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Optimal purely functional priority queues

  • Gerth Stølting Brodal (a1) and Chris Okasaki (a2)
Abstract

Brodal recently introduced the first implementation of imperative priority queues to support findMin, insert and meld in O(1) worst-case time, and deleteMin in O(log n) worst-case time. These bounds are asymptotically optimal among all comparison-based priority queues. In this paper, we adapt Brodal's data structure to a purely functional setting. In doing so, we both simplify the data structure and clarify its relationship to the binomial queues of Vuillemin, which support all four operations in O(log n) time. Specifically, we derive our implementation from binomial queues in three steps: first, we reduce the running time of insert to O(1) by eliminating the possibility of cascading links; second, we reduce the running time of findMin to O(1) by adding a global root to hold the minimum element; and finally, we reduce the running time of meld to O(1) by allowing priority queues to contain other priority queues. Each of these steps is expressed using ML-style functors. The last transformation, known as data-structural bootstrapping, is an interesting application of higher-order functors and recursive structures.

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*Research partially supported by the ESPRIT II Basic Research Actions Program of the EC under contract no. 7141 (project ALCOM II) and by the Danish Natural Science Research Council (Grant No. 9400044).
Research supported by the Advanced Research Projects Agency CSTO under the title “The Fox Project: Advanced Languages for Systems Software”, ARPA Order No. C533, issued by ESC/ENS under Contract No. F19628-95-C-0050.
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Basic Research in Computer Science, Centre of the Danish National Research Foundation.

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References
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Journal of Functional Programming
  • ISSN: 0956-7968
  • EISSN: 1469-7653
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Optimal purely functional priority queues

  • Gerth Stølting Brodal (a1) and Chris Okasaki (a2)
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