Abstract
In this paper we study the computational complexity of constructing implicit, doubleended priority queues organized as min-max heaps, presenting two new algorithms for solving the problem. To construct a min-max heap on n elements, the first one uses 187/96n=1.95 ... n comparisons in the worst case (neglecting lower order terms) and O(n) extra space, while the second one offers a slight improvement in time and space, using (187/96−α)n comparisons, for α ≈ 0.014, i.e., 1.93 ... n comparisons and only O(1) extra space.
The algorithms are particularly interesting as they each have a distinct flavour, even though their time-complexities are virtually identical. The algorithms improve the previously best known upper bound of 2.15 ... n comparisons.
This work was done for the most part while the author was on leave at Institutionen för Teknisk Databehandling, Uppsala Universitet, Sweden.
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© 1988 Springer-Verlag Berlin Heidelberg
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Draws, L., Eriksson, P., Forslund, E., Höglund, L., Vallner, S., Strothotte, T. (1988). Two new algorithms for constructing min-max heaps. In: Karlsson, R., Lingas, A. (eds) SWAT 88. SWAT 1988. Lecture Notes in Computer Science, vol 318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19487-8_5
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DOI: https://doi.org/10.1007/3-540-19487-8_5
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