Abstract
A new priority queue structure is introduced, for which the amortized time to insert a new element is O(1) while that for the minimum-extraction is \(O({\rm log} \bar{K})\). \(\bar{K}\) is the average, taken over all the deleted elements x, of the number of elements that are inserted during the lifespan of x and are still in the heap when x is removed. Several applications of our structure are mentioned.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brown, M.: Implementation and analysis of binomial queue algorithms. SIAM J. Comput. 7, 298–319 (1978)
Brown, M., Tarjan, R.: Design and analysis of data structures for representing sorted lists. SIAM J. Comput. 9, 594–614 (1980)
Carlsson, S., Munro, J.I.: An implicit binomial queue with constant insertion time. 1st SWAT. In: Karlsson, R., Lingas, A. (eds.) SWAT 1988. LNCS, vol. 318, pp. 1–13. Springer, Heidelberg (1988)
Cole, R.: On the dynamic finger conjecture for splay trees. Part II: The proof. SIAM J. Comput. 30, 44–85 (2000)
De Berg, M., Kreveld, M., Overmars, M., Shwarzkopf, O.: Computational geometry-algorithms and applications. Springer, Berlin (1997)
Devroye, L.: Nonuniform random variate generation. Springer, Heidelberg (1986)
Doberkat, E.: Deleting the root of a heap. Acta Informatica 17, 245–265 (1982)
Dutton, R.: Weak-Heapsort. BIT 33, 372–381 (1993)
Edelkamp, S., Wegener, I.: On the performance of weak-heapsort. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 254–260. Springer, Heidelberg (2000)
Elmasry, A.: Priority queues, pairing and adaptive sorting. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 183–194. Springer, Heidelberg (2002)
Elmasry, A.: A new proof for the sequential access theorem for splay trees. WSES, ADISC. Theoretical and Applied Mathematics, pp. 132–136 (2001)
Fredman, M., Sedgewick, R., Sleator, D., Tarjan, R.: The pairing heap: a new form of self adjusting heap. Algorithmica 1(1), 111–129 (1986)
Guibas, L., McCreight, E., Plass, M., Roberts, J.: A new representation of linear lists. ACM STOC 9, 49–60 (1977)
Iacono, J.: Improved upper bounds for pairing heaps. In: 7th SWAT. LNCS, pp. 32–45 (2000)
Iacono, J.: Distribution sensitive data structures. Ph.D. thesis, Rutgers University (2001)
Iacono, J., Langerman, S.: Queaps. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 211–218. Springer, Heidelberg (2002)
Knuth, D.: The Art of Computer Programming, Sorting and Searching, 2nd edn., vol. III. Addison-wesley, Reading (1998)
Mannila, H.: Measures of presortedness and optimal sorting algorithms. IEEE Trans. Comput. C-34, 318–325 (1985)
Porter, T., Simon, I.: Random insertion into a priority queue structure. IEEE Trans. Software Engineering 1 SE, 292–298 (1975)
Sleator, D., Tarjan, R.: Self-adjusting binary search trees. J. ACM 32(3), 652–686 (1985)
Sundar, R.: On the deque conjecture for the splay algorithm. Combinatorica 12, 95–124 (1992)
Tarjan, R.: Sequential access in splay trees takes linear time. Combinatorica 5, 367–378 (1985)
Tarjan, R.: Amortized computational complexity. SIAM J. Alg. Disc. Meth. 6, 306–318 (1985)
Vuillemin, J.: A data structure for manipulating priority queues. Comm. ACM 21(4), 309–314 (1978)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Elmasry, A. (2003). Distribution-Sensitive Binomial Queues. In: Dehne, F., Sack, JR., Smid, M. (eds) Algorithms and Data Structures. WADS 2003. Lecture Notes in Computer Science, vol 2748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45078-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-540-45078-8_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40545-0
Online ISBN: 978-3-540-45078-8
eBook Packages: Springer Book Archive