Two-Tier relaxed heaps

Authors:
Amr Elmasry;Claus Jensen;Jyrki Katajainen
Affiliations:
Department of Computer Engineering and Systems, Alexandria University, Alexandria, Egypt;Department of Computing, University of Copenhagen, Copenhagen East, Denmark;Department of Computing, University of Copenhagen, Copenhagen East, Denmark
Venue:
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Year:
2006

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Abstract

We introduce an adaptation of run-relaxed heaps which provides efficient heap operations with respect to the number of element comparisons performed. Our data structure guarantees the worst-case cost of O(1) for find–min, insert, and decrease; and the worst-case cost of O(lg n) with at most lg n + 3 lg lg n + O(1) element comparisons for delete, improving the bound of $3\lg n + O(1)$ on the number of element comparisons known for run-relaxed heaps. Here, n denotes the number of elements stored prior to the operation in question, and lg n equals max{1, log2n}.