Two-tier relaxed heaps

13 years 5 months ago

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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, log2 n}.

Amr Elmasry, Claus Jensen, Jyrki Katajainen

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