Abstract
We present several simple probabilistic data structures for implementing priority queues. We present a data structure called simple bottom-up sampled heap (SBSH), supporting insert in O(1) expected time and delete, delete minimum, decrease key and meld in O(log n) time with high probability. An extension of SBSH called BSH1, supporting insert and meld in O(1) worst case time is presented. This data structure uses a novel “buffering technique” to improve the expected bounds to worst-case bounds. Another extension of SBSH called BSH2, performing insert, decrease key and meld in O(1) amortized expected time and delete and delete minimum in O(log n) time with high probability is also presented. The amortized performance of this data structure is comparable to that of Fibonacci heaps (in probabilistic terms). Moreover, unlike Fibonacci heaps, each operation takes O(log n) time with high probability, making the data structure suitable for real-time applications.
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C.R.Aragon and R.G. Seidel. Randomized search trees. Proc. 30th Ann. IEEE Symposium on Foundations of Computing, 540–545 (1989)
Gerth Stólting Brodal. Fast meldable priority queues. Proc. 4th International Workshop, WADS, 282–290 (1995)
Gerth Stólting Brodal. Worst-case efficient priority queues. Proc. 7th Ann. ACM Symposium on Discrete Algorithms, 52–58 (1996)
Giorgio Gambosi, Enrico Nardelli, Maurizio Talamo. A Pointer-Free data structure for merging heaps and min-max heaps. Theoritical Computer Science 84(1), 107–126 (1991)
James R. Driscoll, Harold N. Gabow, Ruth Shrairman and Robert E. Tarjan. Relaxed Heaps: An alternative approach to Fibonacci Heaps with applications to parallel computing. Comm. ACM 31(11), 1343–1354 (1988)
Jean Vuillemin. A data structure for manipulating priority queues. Comm. ACM 21(4), 309–315 (1978)
Knuth, D. The Art of Computer Programming, Volume 3, Sorting and Searching. Addison-Wesley, Reading, Mass., 1973
Michael L. Fredman and Robert E. Tarjan Fibonacci heaps and their uses in improved network optimization algorithms. Proc. 25th Annual Symposium on Foundations of Computer Science, 338–346 (1984)
Michiel Smid. Lecture Notes: Selected Topics in Data Structures. Max-Plank Institute for Informatics, Germany.
W. Pugh. Skip lists: A probabilistic alternative to balanced trees. Comm. ACM 33, 668–676 (1990)
P. Raghavan, Lecture notes in randomized algorithms, Technical Report RC15340, IBM J.J.Watson Research Center (1989).
Rolf Fagerberg, A Note on Worst Case Efficient Meldable Priority Queues, Technical Report, Odense University Computer Science Department Preprint 1996-12.
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest. Introduction to Algorithms. The MIT Press, Cambridge, Massachusetts (1989)
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© 1998 Springer-Verlag Berlin Heidelberg
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Sridhar, R., Rajasekar, K., Rangan, C.P. (1998). Probabilistic data structures for priority queues. In: Arnborg, S., Ivansson, L. (eds) Algorithm Theory — SWAT'98. SWAT 1998. Lecture Notes in Computer Science, vol 1432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054362
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DOI: https://doi.org/10.1007/BFb0054362
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