A data structure called aweak-heap is defined by relaxing the requirements for a heap. The structure can be implemented on a 1-dimensional array with one extra bit per data item and can be initialized withn items using exactlyn−1 data element compares. Theoretical analysis and empirical results indicate that it is a competitive structure for sorting. The worst case number of data element comparisons is strictly less than (n−1) logn+0.086013n and the expected number is conjectured to be approximately (n−0.5)logn−0.413n.
CR CategoriesE.1 F2.2
KeywordsAlgorithms data structures heap priority queue
Unable to display preview. Download preview PDF.
- 1.S. Carlsson,Average-case results on heapsort, BIT, 27, 1987, pp. 2–17.Google Scholar
- 2.S. Carlsson, J. I. Munro and P. V. Poblete,An implicit binomial queue with constant insertion time, Proceedings of 1st Scandinavian Workshop on Algorithm Theory, Halmstad, Sweden, July 5–8, 1988, pp. 1–13.Google Scholar
- 3.R. D. Dutton,The weak-heap data structure, Department of Computer Science Technical Report, CS-TR-92-09, 1992, University of Central Florida, Orlando, FL 32816.Google Scholar
- 4.R. W. Floyd,Algorithm 245,treesort 3, Comm. ACM, 1964, p. 701.Google Scholar
- 5.C. A. R. Hoare,Algorithm 63, 64and 65, Comm. ACM, 4 (7), 1961, pp. 321–322.Google Scholar
- 6.C. J. H. McDiarmid and B. A. Reed,Building heaps fast, J. of Algorithms, 10, 1989, pp. 352–365.Google Scholar
- 7.J. R. Sack and T. Strothotte,An algorithm for merging heaps, Acta Informatica 22, 1985, pp. 171–186.Google Scholar
- 8.J. Vuillemin,A data structure for manipulating priority queues, Comm. of the ACM, 21 (4), 1978, pp. 309–315.Google Scholar
- 9.I. Wegener,Bottom-up heap sort, a new variant of heap sort beating on average quicksort (if n is not very small), Proceedings of Mathematical Foundations of Computer Science 1990, Banska Bystrica, Czechoslovakia, August, 1990, pp. 516–522.Google Scholar
- 10.I. Wegener,The worst case complexity of McDiarmid and Reed's variant of Bottom-Up heapsort is less than n logn+1.1n, Information and Computation, 97, 1992, pp. 86–96.Google Scholar
- 11.J. W. J. Williams,Algorithm 232,Heapsort, Comm. of the ACM, 7, 1964, pp. 347–348.Google Scholar