Comparator networks for binary heap construction
Comparator networks for constructing binary heaps of size n are presented which have size O(n log log n) and depth O(log n). A lower bound of n log log n — O(n) for the size of any heap construction network is also proven, implying that the networks presented are within a constant factor of optimal. We give a tight relation between the leading constants in the size of selection networks and in the size of heap construction networks.
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- 2.Vladimir Evgen'evich Alekseev. Sorting algorithms with minimum memory. Kibernetika, 5(5):99–103, 1969.Google Scholar
- 3.Samuel W. Bent and John W. John. Finding the median requires 2n comparisons. In Proc. 17th Ann. ACM Symp. on Theory of Computing (STOC), pages 213–216, 1985.Google Scholar
- 5.Paul F. Dietz. Heap construction in the parallel comparison tree model. In Proc. 3rd Scandinavian Workshop on Algorithm Theory (SWAT), volume 621 of Lecture Notes in Computer Science, pages 140–150. Springer Verlag, Berlin, 1992.Google Scholar
- 6.Paul F. Dietz and Rajeev Raman. Very fast optimal parallel algorithms for heap construction. In Proc. 6th Symposium on Parallel and Distributed Processing, pages 514–521, 1994.Google Scholar
- 7.Dorit Dor and Uri Zwick. Selecting the median. In Proc. 6th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 28–37, 1995.Google Scholar
- 9.Dorit Dor and Uri Zwick. Median selection requires (2 + ε)n comparisons. In Proc. 37th Ann. Symp. on Foundations of Computer Science (FOCS), pages 125–134, 1996.Google Scholar
- 12.Donald E. Knuth. The Art of Computer Programming, Volume III: Sorting and Searching. Addison-Wesley, Reading, MA, 1973.Google Scholar
- 17.John William Joseph Williams. Algorithm 232: Heapsort. Communications of the ACM, 7(6):347–348, 1964.Google Scholar