Advertisement

A Unifying Property for Distribution-Sensitive Priority Queues

  • Amr Elmasry
  • Arash Farzan
  • John Iacono
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7056)

Abstract

We present a priority queue that supports the operations: insert in worst-case constant time, and delete, delete-min, find-min and decrease-key on an element x in worst-case \(O(\lg(\min\{w_x, q_x\}+2))\) time, where w x (respectively, q x ) is the number of elements that were accessed after (respectively, before) the last access of x and are still in the priority queue at the time when the corresponding operation is performed. Our priority queue then has both the working-set and the queueish properties; and, more strongly, it satisfies these properties in the worst-case sense. We also argue that these bounds are the best possible with respect to the considered measures. Moreover, we modify our priority queue to satisfy a new unifying property — the time-finger property — which encapsulates both the working-set and the queueish properties.

In addition, we prove that the working-set bound is asymptotically equivalent to the unified bound (which is the minimum per operation among the static-finger, static-optimality, and working-set bounds). This latter result is of tremendous interest by itself as it had gone unnoticed since the introduction of such bounds by Sleater and Tarjan [10].

Together, these results indicate that our priority queue also satisfies the static-finger, the static-optimality and the unified bounds.

Keywords

Minimum Element Priority Queue Binomial Tree Interleave Sequence Implication Relationship 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bdoiu, M., Cole, R., Demaine, E.D., Iacono, J.: A Unified Access Bound on Comparison-based Dynamic Dictionaries. Theoretical Computer Science 382(2), 86–96 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Brodal, G.S., Fagerberg, R.: Funnel Heap - a Cache Oblivious Priority Queue. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 219–228. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Cole, R.: On the Dynamic Finger Conjecture for Splay Trees. Part II: Finger Searching. SIAM Journal on Computing 30, 44–85 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Elmasry, A.: On the Sequential Access Theorem and Dequeue Conjecture for Splay Trees. Theoretical Computer Science 314(3), 459–466 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Elmasry, A.: A Priority Queue with the Working-set Property. International Journal of Foundation of Computer Science 17(6), 1455–1466 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Fredman, M.L., Sedgewick, R., Sleator, D.D., Tarjan, R.E.: The Pairing Heap: a New Form of Self-adjusting Heap. Algorithmica 1(1), 111–129 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Lacono, J.: Improved Upper Bounds for Pairing Heaps. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 32–45. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Iacono, J.: Distribution-sensitive Data Structures. Ph.D. thesis, Rutgers, The state University of New Jersey, New Brunswick, New Jersey (2001)Google Scholar
  9. 9.
    Iacono, J., Langerman, S.: Queaps. Algorithmica 42(1), 49–56 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Sleator, D.D., Tarjan, R.E.: Self-adjusting Binary Search Trees. Journal of the ACM 32(3), 652–686 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Tarjan, R.E.: Sequential Access in Splay Trees Takes Linear Time. Combinatorica 5(4), 367–378 (1985)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Amr Elmasry
    • 1
  • Arash Farzan
    • 2
  • John Iacono
    • 3
  1. 1.Computer Science DepartmentUniversity of CopenhagenDenmark
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany
  3. 3.Polytechnic Institute of New York UniverityBrooklynUSA

Personalised recommendations