Abstract
A sorting algorithm is adaptive [15, page 224]_if it requires fewer comparisons to sort a “nearly-sorted” sequence than to sort a “well-shuffled” sequence. Adaptive sorting algorithms are attractive because nearly sorted sequences are common in practice [10,15]. Recently, adaptive sorting has been the subject of intensive investigation [6, 11, 12, 14, 18, 19]. However, the proposed sorting algorithms have received limited acceptance because they are adaptive with respect to only one or two measures [2, 6, 8, 12, 18], they require complex data structures that have a significant overhead [3, 11, 14], or their adaptive behavior has eluded analysis [2, 4, 19]. Moreover, the analysis of the performance of adaptive algorithms has been, so far, based only on worst-case. The notion of optimal adaptivity in the worst case was formalized by Mannila [14]_who quantified disorder with measures of presortedness.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. Aragon and R. Seidel. Randomized search trees. In Proceedings of the 30th IEEE Symposium on Foundations of Computer Science, pages 540–545, Research Triangle Park, NC, 1989.
CR. Cook and D.J. Kim. Best sorting algorithms for nearly sorted lists. Communications of the ACM, 23:620–624, 1980.
E.W. Dijkstra. Smoothsort, an alternative to sorting in situ. Science of Computer Programming, 1:223–233, 1982.
P.G. Dromey. Exploiting partial order with Quicksort. Software — Practice and Experience, 14(6):509–518, 1984.
V. Estivill-Castro. Sorting and Measures of Disorder. PhD thesis, University of Waterloo, 1991. Available as Department of Computer Science Research Report CS-91-07.
V. Est ivill-Castro and D. Wood. A new measure of presortedness. Information and Computation, 83:111–119, 1989.
S. L. Graham, P.B. Kessler, and M. K. McKusik. gprof: A call graph execution profiler. The Proceedings of the SIGPLAN’82 Symposium on Compiler Construction, SIGPLAN Notices, 17(6):120–126, 1982.
J. D. Harris. Sorting unsorted and partially sorted lists using the natural merge sort. Software — Practice and Experience, 11:1339–1340, 1981.
J. Katajainen and H. Mannila. On average case optimality of a presorting algorithm. Unpublished manuscript, 1989.
D.E. Knuth. The Art of Computer Programming, Vol.3: Sorting and Searching. Addison-Wesley Publishing Co.,Reading, Mass., 19
C Levcopoulos and O. Petersson. Heapsort — adapted for presorted files. In F. Dehne, J.R. Sack, and N. Santoro, editors, Proceedings of the Workshop on Algorithms and Data Structures, pages 499–509. Springer-Verlag Lecture Notes in Computer Science 382, 1989.
C. Levcopoulos and O. Petersson. (atSplitsort—an adaptive sorting algorithm. In B. Rovan, editor, Mathematical Foundations of Computer Science, pages 416–422. Springer-Verlag Lecture Notes in Computer Science 452, 1990.
M. Li and P.M.B. Vitanyi. (atA theory of learning simple concepts under simple distributions and average case complexity for the universal distribution. In Proceedings of the 30th IEEE Symposium on Foundations of Computer Science, pages 34–39, Research Triangle Park, NC, 1989.
H. Mannila. (atMeasures of presortedness and optimal sorting algorithms. IEEE Transactions on Computers, C-34:318–325, 1985.
K. Mehlhorn. Data Structures and Algorithms, Vol 1: Sorting and Searching. EATCS Monographs on Theoretical Computer Science. Springer-Verlag, Berlin/Heidelberg, 1984.
T. Papadakis, J. I. Munro, and P.V. Poblete. (atAnalysis of the Expected Search Cost in Skip Lists. In J.R. Gilbert and R. Karlsson, editors, Proceedings of the 2nd Scandinavian Workshop on Algorithm Theory, pages 160–172, Bergen, Sweden, 1990. Springer-Verlag Lecture Notes in Computer Science 447.
W. Pugh. Skip Lists: A probabilistic alternative to balanced trees. Communications of the ACM, 33(6):668–676, 199
S.S. Skiena. (atEncroaching lists as a measure of presortedness. BIT, 28:755–784, 1988.
R.L. Wainwright. A class of sorting algorithms based on Quicksort. Communications of the ACM, 28:396–402, 85.
A.C. Yao. (atProbabilistic computations — toward a unified measure of complexity. In Proceedings of the 18th IEEE Symposium on Foundations of Computer Science, pages 222–227, 1977.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media New York
About this chapter
Cite this chapter
Estivill-Castro, V., Wood, D. (1992). Skip Sort — An Adaptive Randomized Algorithm or Expected Time Adaptivity is Best. In: Baeza-Yates, R., Manber, U. (eds) Computer Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3422-8_17
Download citation
DOI: https://doi.org/10.1007/978-1-4615-3422-8_17
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6513-6
Online ISBN: 978-1-4615-3422-8
eBook Packages: Springer Book Archive