Optimal Purely Functional Priority Queues

Optimal Purely Functional Priority Queues (1996)

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by Gerth Stølting Brodal , Gerth St��lting Brodal , Chris Okasaki

Venue:	Journal of Functional Programming
Citations:	16 - 1 self

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@ARTICLE{Brodal96optimalpurely,
    author = {Gerth Stølting Brodal and Gerth St��lting Brodal and Chris Okasaki},
    title = {Optimal Purely Functional Priority Queues},
    journal = {Journal of Functional Programming},
    year = {1996},
    volume = {6},
    pages = {839--857}
}

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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) worstcase 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 transfo...

Keyphrases

optimal purely functional priority queue running time binomial queue data structure priority queue ml-style functors worstcase time minimum element first implementation functional setting last transfo comparison-based priority queue global root worst-case time imperative priority queue