Abstract
In this paper a data structure for the representation of mergeable heaps and min-max heaps without using pointers is introduced. The supported operations are: Insert, Deletemax, Deletemin, Findmax, Findmin, Merge, Newheap, Deleteheap. The structure is analysed in terms of amortized time complexity, resulting in a O(1) amortized time for each operation but for Insert, for which a O(lgN) bound holds.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
7. References
H. Alt, K. Mehlhorn, J.I. Munro, "Partial match retrieval in implicit data structures", Inf. Proc. Let., 19, 2, (1984).
A.V. Aho, J.E. Hopcroft, J.D. Ullman, The design and analysis of computer algorithms, Addison-Wesley, Reading, Ma., (1974).
M.D. Atkinson, J.R. Sack, N. Santoro, T. Strothotte "Min-Max heaps and generalized priority queues" Comm. A.C.M., 29, 10, (1986).
A. Borodin, L.J. Guibas, N.A. Lynch, A.C. Yao, "Efficient searching using partial ordering", Inf. Proc. Let., 12, 2, (1981).
A.Borodin, F.E.Fich, F.Meyer auf der Heide, E.Upfal, A.Widgerson, "A tradeoff between search and update time for the implicit dictionary problem", 13th ICALP, Rennes, France, (1986).
J.L.Bentley, J.B.Saxe "Decomposable searching problems I. Static to dynamic transformation" J. of Algorithms, 1, (1980).
D. Cheriton, R.E. Tarjan "Finding minimum spanning trees" SIAM J. Comput., 5, 4, (1976).
G.N. Frederickson "Implicit data structures for the dictionary problem" J. Ass. Comp. Mach., 30, 1, (1983).
G.N. Frederickson "Recursively rotated orders and implicit data structures: a lower bound" Theoret. Comp. Sci., 29, 1, (1984).
M.L. Fredman, R.E. Tarjan "Fibonacci heaps and their uses in improved network optimization algorithms", J. Ass. Comp. Mach., 34, 3, (1987).
D.E. Knuth, The art of computer programming, volume 3: sorting and searching, Addison-Wesley, Reading, Ma., (1973).
J.I. Munro, H. Suwanda "Implicit data structures for fast search and update" J. Comp. Syst. Sci., 21, 2, (1980).
J.I. Munro "An implicit data structure supporting insertion, deletion and search in O(lg2n) time" J. Comp. Syst. Sci., 33, 1, (1986).
J.R.Sack, T.Strothotte "An algorithm for merging heaps" Acta Informatica 22, (1985).
R.E. Tarjan, Data Structures and Network Algorithms, CBMS Regional Conference Series in Applied Mathematics 44, SIAM, Philadelphia, (1983).
R.E. Tarjan "Amortized Computational Complexity" SIAM J. Alg. Disc. Meth., 6, 2, (1985).
J.W.J.Williams "Algorithm 232: Heapsort" Comm. Ass. Comp. Mach., 7, (1964).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gambosi, G., Nardelli, E., Talamo, M. (1989). A pointer-free data structure for merging heaps and min-max heaps. In: Ausiello, G., Dezani-Ciancaglini, M., Della Rocca, S.R. (eds) Automata, Languages and Programming. ICALP 1989. Lecture Notes in Computer Science, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035773
Download citation
DOI: https://doi.org/10.1007/BFb0035773
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51371-1
Online ISBN: 978-3-540-46201-9
eBook Packages: Springer Book Archive