# An Improvement on Tree Selection Sort

Conference paper

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## Abstract

The standard Tree Selection Sort is an efficient sorting algorithm but requires extra storage for *n*-1 pointers and *n* items. The goal of this paper is to not only reduce the extra storage of Tree Selection Sort to *n* bits, but also keep the number of comparisons at *n*log*n*+*O*(*n*). The improved algorithm makes at most 3*n* data movements. The empirical results show that the improved algorithm is efficient. In some cases, say moving one item requires at least 3 assignment operations, the algorithm is the fastest on average among known fast algorithms.

## Keywords

Data Movement Internal Node Space Requirement Selection Phase Sorting Algorithm
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.

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## References

- 1.J.W.J. Williams, Algorithm 232, Heapsort 3, Comm.ACM, 7, 1964, pp. 347–348.Google Scholar
- 2.R.W. Floyd, Algorithm 245, Treesort 3, Comm.ACM, 1964, p. 701.Google Scholar
- 3.C.A.R. Hoare, Algorithm 63,64 and 65, Comm.ACM, 4(7), 1961,pp. 321–322.CrossRefGoogle Scholar
- 4.E.H. Friend, Sorting on electronic computers, JACM 3(2), 1956, pp. 34–168.Google Scholar
- 5.D.E. Knuth, “The Art of Computer Programming Vol.3: Sorting and Searching”, Addison-Wesley, Reading, MA, 1973Google Scholar
- 6.I. Wegener, The worst case complexity of McDiarmid and Reed’s variant of Bottom-Up heapsort is less than nlogn+1.1n, information and computation, 97, 1992, pp. 86–96.zbMATHCrossRefMathSciNetGoogle Scholar
- 7.C.J.H. McDiarmid and B.A. Reed, Building heaps fast, J. Algorithms 10, pp. 352–369.Google Scholar
- 8.S. Carlsson, A variant of heapsort with almost optimal number of comparisons, Inform. Process. Lett. 24, pp. 247–250.Google Scholar
- 9.G.H. Gonnet and J.I. Munro, Heaps on heaps, Proc. 9th ICALP, Aarhus, Denmark, July 12–16, 1982,pp. 282–291.Google Scholar
- 10.R.D. Dutton, Weak-heap sort, BIT 33, 1993,pp. 372–381.CrossRefMathSciNetGoogle Scholar
- 11.J.C. Chen, Proportion split sort, Nordic Journal of Computing 3(1996), pp. 271–279.Google Scholar
- 12.J.C. Chen, Proportion extend sort, SIAM Journal on Computing, Vol. 31, No. 1, 2001, pp. 323–330.zbMATHCrossRefMathSciNetGoogle Scholar
- 13.A. LaMarca and R.E. Lader, The influence of Caches on the performance of sorting, J. Algorithms 31, 1999, pp. 66–104.zbMATHCrossRefMathSciNetGoogle Scholar
- 14.R. Sedgewick, Implementing quicksort programs. Communications of the ACM, 21(10), pp. 847–857, October, 1978.Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 2002