Abstract
Until recently, it was not known whether it was possible to stably sort (Le. keeping equal elements in their initial order) an array of n elements using only O(n) data movements and O(1) extra space. In [10], an algorithm was given to perform this task in O(n 2) comparisons in the worst case. Here, we develop a new algorithm for the problem that performs only O(n 1+ε) comparisons (0<ε<1 is any fixed constant) in the worst case. This bound on the number of comparisons matches (asymptotically) the best known bound for the same problem with the stability constraint dropped.
Research supported by Natural Sciences and Engineering Research Council of Canada grant No. A-8237 and the Information Technology Research Centre of Ontario
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References
E. H. Friend, Sorting on Electronic Computers, Journal of the ACM, 3(2) (1956) 134–168.
B. C. Huang and M. A. Langston, Practical In-place Merging, Communications of the ACM, 31(3) (1988) 348–352.
B. C. Huang and M. A. Langston, Fast Stable Merging and Sorting in Constant Extra Space, Computing and Information, (1989), 71–79.
D. E. Knuth, The Art of Computer Programming. Volume III: Sorting and Searching, Addison-Wesley (1973).
M. A. Kronrod, Optimal Ordering Algorithm without Operational Field, Soviet Math. Dokl. 10 (1969) 744–746.
T. W. Lai and D. Wood, Implicit Selection, Proceedings of the Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science 318, Springer Verlag, (1988) 14–23.
J. I. Munro, An Implicit Data Structure Supporting Insertion, Deletion, and Search in O(lg 2n) time, Journal of Computer and System Sciences, 21 (1980) 236–250.
J. I. Munro and V. Raman, Sorting with Minimum Data Movement, Proceedings of Workshop on Algorithms and Data Structures, Ottawa, Lecture Notes in Computer Science, Springer Verlag 382 (1989) 552–562; (revised version to appear in Journal of Algorithms)
J. I. Munro and V. Raman, Selection in Read-Only Memory and Sorting with Optimum Data Movement, submitted for publication.
J. I. Munro, V. Raman and J. S. Salowe, Stable In Situ Sorting and Minimum Data Movement, BIT 30 (1990) 220–234.
V. Raman, Sorting In-Place with Minimum Data Movement, Ph.D. Thesis, Technical Report CS 91-12, Department of Computer Science, University of Waterloo (1991).
L. Trabb Pardo, Stable Sorting and Merging with Optimal Space and Time Bounds, SIAM J. of Computing 6 (1977) 351–372.
J. W. J. Williams, Algorithm 232, Heapsort, Communications of the ACM, 7 (1964) 347–348.
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© 1991 Springer-Verlag Berlin Heidelberg
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Munro, J.I., Raman, V. (1991). Fast stable in-place sorting with O(n) data moves. In: Biswas, S., Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1991. Lecture Notes in Computer Science, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54967-6_74
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DOI: https://doi.org/10.1007/3-540-54967-6_74
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