Abstract
In this paper we show that to construct an implicit, double-ended priority queue organized as a min-max heap, 17/9n = 1.88 ...n comparisons suffice in the worst case (neglectng lower order terms). The algorithm improves the previously best known upper bound of 2.15 ...n comparisons.
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M. D. Atkinson, J.-R. Sack, N. Santoro, and Th. Strothotte:Min-max heaps and generalized priority queues. Communications of the ACM, 29 (10): 996–1000, October 1986.
S. Carlsson:Average-case analysis of operation on heaps. BIT, 27 (1): 2–17, 1987.
S. Carlsson:The deap-a double-ended heap to implement double-ended priority queues. Information Processing Letters, 26 (1): 33–36, September 1987.
S. Carlsson:Heaps. PhD thesis, Department of Computer Science, Lund University, November 1986.
S. Carlsson, J. Chen, and Th. Strothotte:A note on the construction of the data structure ‘deap’. Information Processing Letters, 1989. (to appear).
E. Doberkat:On deleting the root of a heap. Acta Informatica, 17: 245–265, 1982.
L. Draws, P. Eriksson, E. Forslund, L. Höglund, S. Vallner, and Th. Strothotte:Two new algorithms for constructing min-max heaps. In A. Lingas and R. Karlsson, editors,1st Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, 318: 43–50, Springer-Verlag, Berlin-Heidelberg-New York, 1988.
R. W. Floyd:Algorithm 245 — treesort 3. Communications of the ACM, 7 (12): 701, 1964.
A. M. Frieze:On the random construction of heaps. Information Processing Letters, 27 (2): 103–109, February 1988.
G. H. Gonnet:Handbook of Algorithms and Data Structures. Addison-Wesley, Reading, MA., 1984.
G. H. Gonnet and J. I. Munro:Heaps on heaps. SIAM Journal on Computing, 15 (4): 964–971, November 1986.
A. Hasham and J.-R. Sack:Bounds for min-max heaps. BIT 27 (12): 315–323, 1987.
Donald E. Knuth:The Art of Computer Programming. Volume 3, Addison-Wesley, Reading, MA, 1973.
C. J. H. McDiarmid and B. A. Reed:Building Heaps Fast. Technical Report, Oxford University, 1987.
J.-R. Sack and Th. Strothotte:An algorithm for merging heaps. Acta Informatica, 22: 171–185, 1985.
Th. Strothotte and J.-R. Sack:Heaps in heaps. Congressus Numerantium, 49: 223–235, 1985.
J. W. J. Williams:Algorithm 232. Communications of the ACM, 7 (6): 347–348, 1964.
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Some of the ideas given in this paper were presented in a preliminary form at the 1st Scandinavian Workshop on Algorithm Theory, Halmstad (July, 1988) [7].
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Strothotte, T., Eriksson, P. & Vallner, S. A note on constructing min-max heaps. BIT 29, 251–256 (1989). https://doi.org/10.1007/BF01952680
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DOI: https://doi.org/10.1007/BF01952680