Why some heaps support constant-amortized-time decrease-key operations, and others do not

John Iacono, Özgür Özkan

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    A lower bound is presented which shows that a class of heap algorithms in the pointer model with only heap pointers must spend Ω(log log n/log log log n) amortized time on the Decrease-Key operation (given O(logn) amortized-time Extract-Min). Intuitively, this bound shows the key to having O(1)-time Decrease-Key is the ability to sort O(logn) items in O(logn) time; Fibonacci heaps [M. .L. Fredman and R. E. Tarjan. J. ACM 34(3):596-615 (1987)] do this through the use of bucket sort. Our lower bound also holds no matter how much data is augmented; this is in contrast to the lower bound of Fredman [J. ACM 46(4):473-501 (1999)] who showed a tradeoff between the number of augmented bits and the amortized cost of Decrease-Key. A new heap data structure, the sort heap, is presented. This heap is a simplification of the heap of Elmasry [SODA 2009: 471-476] and shares with it a O(loglogn) amortized-time Decrease-Key, but with a straightforward implementation such that our lower bound holds. Thus a natural model is presented for a pointer-based heap such that the amortized runtime of a self-adjusting structure and amortized lower asymptotic bounds for Decrease-Key differ by but a O(logloglogn) factor.

    Original languageEnglish (US)
    Title of host publicationAutomata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings
    PublisherSpringer Verlag
    Pages637-649
    Number of pages13
    EditionPART 1
    ISBN (Print)9783662439470
    DOIs
    StatePublished - Jan 1 2014
    Event41st International Colloquium on Automata, Languages, and Programming, ICALP 2014 - Copenhagen, Denmark
    Duration: Jul 8 2014Jul 11 2014

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    NumberPART 1
    Volume8572 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other41st International Colloquium on Automata, Languages, and Programming, ICALP 2014
    CountryDenmark
    CityCopenhagen
    Period7/8/147/11/14

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    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Iacono, J., & Özkan, Ö. (2014). Why some heaps support constant-amortized-time decrease-key operations, and others do not. In Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings (PART 1 ed., pp. 637-649). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8572 LNCS, No. PART 1). Springer Verlag. https://doi.org/10.1007/978-3-662-43948-7_53