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Why Some Heaps Support Constant-Amortized-Time Decrease-Key Operations, and Others Do Not

  • John Iacono
  • Özgür Özkan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8572)

Abstract

A lower bound is presented which shows that a class of heap algorithms in the pointer model with only heap pointers must spend \(\Omega \left( \frac{\log \log n}{\log \log \log n} \right)\) 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.

Keywords

Terminal Structure Marked Node Fibonacci Heap Bucket Sort Leftmost Child 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • John Iacono
    • 1
  • Özgür Özkan
    • 1
  1. 1.New York UniversityUSA

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