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}.
Partially supported by the Danish Natural Science Research Council under contracts 21-02-0501 (project Practical data structures and algorithms) and 272-05-0272 (project Generic programming—algorithms and tools).
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Elmasry, A., Jensen, C., Katajainen, J. (2006). Two-Tier Relaxed Heaps. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_32
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DOI: https://doi.org/10.1007/11940128_32
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