Abstract
A data structure that implements a mergeable double-ended priority queue, namely therelaxed min-max heap, is presented. A relaxed min-max heap ofn items can be constructed inO(n) time. In the worst case, operationsfind_min() andfind_max() can be performed in constant time, while each of the operationsmerge(),insert(),delete_min(),delete_max(),decrease_key(), anddelete_key() can be performed inO(logn) time. Moreover,insert() hasO(1) amortized running time. If lazy merging is used,merge() will also haveO(1) worst-case and amortized time. The relaxed min-max heap is the first data structure that achieves these bounds using only two pointers (puls one bit) per item.
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References
[ASSS86] Atkinson, M., Sack, J., Santoro, N., Strothotte, T.: Min-max heaps, and generalized priority queues. Commun. ACM29, 996–1000 (1986)
[B78] Brown, M.: Implementation and analysis of binomial queue algorithms. SIAM J. Comput.7, 298–319 (1978)
[C87] Carlsson, S.: The deap — a double-ended heap to implement double-ended priority queues. Inf. Process. Lett.26, 33–36 (1987)
[DGST88] Driscoll, J., Gabow, H., Shrairman, R.: Relaxed Heaps: An alternative to fibonacci heaps with applications to parallel computation. Commun. ACM31, 1343–1354 (1988)
[F64] Floyd, R.: Algorithm 245: Treesort. Commun. ACM7, 701 (1964)
[FSST86] Fredman, M., Sedgewick, R., Sleator, D., Tarjan, R.: The pairing heap: a new form of self-adjusting heap. Algorithmica1, 111–129 (1986)
[FT87] Fredman, M., Tarjan, R.: Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM34, 596–615 (1987)
[GNT91] Gambosi, G., Nardelli, E., Talamo, M.: A pointer-free data structure for merging heaps and min-max heaps. Theor. Comput. Sci.84, 107–126 (1991)
[HS87] Hasham, A., Sack, J.: Bounds for min-max heaps. BIT27, 315–323 (1987)
[K73] Knuth, D.: The art of computer programming, vol. 3. Reading, MA: Addison-Wesley 1973
[OOW91] Olariu, S., Overstreet, C., Wen, Z.: A mergeable double-ended priority queue. Comput. J.34, 423–427 (1991)
[SS85] Sack, J., Strothotte, T.: An algorithm for merging heaps. Acta Inf.22, 171–186 (1985)
[ST86] Sleator, D., Tarjan, R.: Self-adjusting heaps. SIAM J. Comput.15, 52–69 (1986)
[V78] Vuillemin, J.: A data structure for manipulating priority queues. Commun. ACM21, 309–315 (1978)
[W64] Williams, J.: Algorithm 232: Heapsort. Commun. ACM7, 347–348 (1964)
[W92] Weiss, M.A.: Data structures and algorithm analysis. Redwood City, CA: Benjamin/Cummings 1992
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This research was carried out in summer 1991 when the author was with Florida International University
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Ding, Y., Weiss, M.A. The relaxed min-max heap. Acta Informatica 30, 215–231 (1993). https://doi.org/10.1007/BF01179371
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DOI: https://doi.org/10.1007/BF01179371