An efficient algorithm for the approximate median selection problem

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1767, Issue , 2000, Pages 226-238

  Battiato, Sebastiano ^a   Cantone, Domenico ^a   Catalano, Dario ^a   Cincotti, Gianluca ^a   Hofri, Micha ^b  

^a UNIVERSITY OF CATANIA   (Italy)

^b WORCESTER POLYTECHNIC INSTITUTE   (United States)

Author keywords

Analysis of algorithms; Approximation algorithms; In place algorithms; Median selection

Indexed keywords

GENETIC ALGORITHMS;

ANALYSIS OF ALGORITHMS; ANALYTICAL RESULTS; HIGH PROBABILITY; IN-PLACE ALGORITHMS; LARGE ARRAYS; MEDIAN SELECTIONS; RUNNING TIME;

APPROXIMATION ALGORITHMS;

EID: 84912079268     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-46521-9_19     Document Type: Article

References (27)

1. [AHU74] A.V. Aho, J.E. Hopcroft, and J.D. Ullman. The Design and Analysis of Computer algorithms. Addison Wesley, Reading, MA 1974.
2. [BB96] G. Brassard and P. Bratley. Fundamentals of Algorithmics. Prentice-Hall, Englewood Cliffs, NJ 1996.
3. [BCC*99] S. Battiato, D. Cantone, D. Catalano, G. Cincotti, and M. Hofri. An Efficient Algorithm for the Approximate Median Selection Problem. Technical Report WPI- CS-TR-99-26, Worcester Polytechnic Institute, October 1999. Available from ftp://ftp.es.wpi.edu/pub/techreports/99-26.ps.gz.
4. [BFP*73] M. Blum, R.W. Floyd, V. Pratt, R.L. Rivest, and R. Tarjan. Time bounds for selection. Journal of Computer and Systems Sciences, 7(4):448-461, 1973.
5. [CS87] S. Carlsson, M. Sundstrom. Linear-time In-place Selection in Less than 3 n Comparisons - Division of Computer Science, Lulea University of Technology, S-971 87 LULEA, Sweden.
6. [CLR90] T.H. Cormen, C.E. Leiserson, and R.L. Rivest. Introduction to Algorithms. McGraw- Hill, 1990.
7. [CM89] W. Cunto and J.I. Munro. Average case selection. Journal of the ACM, 36(2):270- 279, 1989.
8. [Dra67] Alvin W. Drake. Fundamentals of Applied Probability Theory. McGraw-Hill, 1967.
9. [DZ99] D. Dor, and U. Zwick. Selecting the Median. SIAM Jour. Comp., 28(5): 1722-1758, 1999.
10. [FJ80] G.N. Frederickson, D.B. Johnson. Generalized Selection and Ranking. Proceedings STOC-SIGACT, Los Angeles CA, 12:420-428, 1980.
11. [Fre90] G.N. Frederickson. The Information Theory Bound is Tight for selection in a heap. Proceedings STOC-SIGACT, Baltimore MD, 22:26-33, 1990.
12. [FR75] R.W. Floyd, R.L. Rivest. Expected time bounds for selection. Communications of the ACM, 18(3): 165-172, 1975.
13. [Hoa61] C.A.R. Hoare. Algorithm 63(partition) and algorithm 65(find). Communications of the ACM, 4(7):321-322, 1961.
14. [Hof95] M. Hofri, Analysis of Algorithms: Computational Methods & Mathematical Tools, Oxford University Press, New York (1995).
15. [HM95] C. Hurley and Reza Modarres: Low-Storage quantile estimation, Computational Statistics, 10:311-325, 1995.
16. [HPM97] P. Kirschenhofer, C. Martinez, and H. Prodinger. Analysis of Hoare's Find algorithm with median-of-three partition. Random Structures and Algorithms, 10:143-156, 1997.
17. [Kat96] J. Katajainen. The Ultimate Heapsort, DIKU Report 96/42, Department of Computer Science, Univ. of Copenhagen, 1996.
18. [Knu98] D.E. Knuth. The Art of Computer Programming, volume 3: Sorting and Searching. Addison-Wesley, 2nd Ed. 1999.
19. [LW88] T.W. Lai, and D. Wood. Implicit Selection. Scandinavian Workshop on Algorithm Theory (SWAT88) :18-23, LNCS 38 Springer-Verlag, 1988.
20. [Meh84] K. Mehlhorn. Sorting and Searching, Data Structures and Algorithms, volume 1. Springer-Verlag, 1984.
21. [Noz73] A. Nozaky. Two Entropies of a Generalized Sorting Problems. Journal of Computer and Systems Sciences, 7(5):615-621, 1973.
22. [PM88] S. K. Park and K. W. Miller. Random number generators: good ones are hard to find. Communications of the ACM, 31(10): 1192-1201, 1988. Updated in Communications of the ACM, 36(7):108-110, 1993.
23. [Ros97] L. Rosaz.Improving Katajainen's Ultimate Heapsort, Technical Report N.1115, Laboratoire de Recherche en Informatique, Université de Paris Sud, Orsay, 1997.
24. [RB90] P.J. Rousseeuw and G.W. Bassett: The remedian: A robust averaging method for large data sets. Jour. Amer. Statist. Assoc, 409:97-104, 1990.
25. [SJ99] Savante Janson - Private communication, June 1999.
26. [SPP76] A. Schonhage, M. Paterson, and N. Pippenger. Finding the median. Journal of Computer and Systems Sciences, 13:184-199, 1976.
27. [Wei78] B. W. Weide. Space efficient on-line selection algorithm. Proceedings of the 11th symposium of Computer Science and Statistics, on the interface, 308-311. (1978).