Abstract
It is possible to improve the worst-case behavior of operations on heaps, when counting number of comparisons between elements in the heap, by modifying the traditional binary heap. The improvement suggested is the use of a heap with “scattered” leaves. This method can be combined with the use of a ternary heap for even greater improvement.
Some other improvements of worst-case behavior compared to standard algorithms are discussed at the end of the paper, where the gain of at least (N-2) comparisons when sortingN elements with HEAPSORT is of great interest in implementations. An algorithm for inserting a new element in a heap inO(log logn) comparisons between elements is mentioned.
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References
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Carlsson, S. Improving worst-case behavior of heaps. BIT 24, 14–18 (1984). https://doi.org/10.1007/BF01934511
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DOI: https://doi.org/10.1007/BF01934511