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The Complexity of Identifying Large Equivalence Classes (1998)  (Make Corrections)  (2 citations)
Peter G. Binderup, Gudmund Skovbjerg Frandsen, Peter Bro Miltersen, Sven Skyum
BRICS, University of Aarhus, DK



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Abstract: We prove that at least - O(k) equivalence tests and no more than + O(n) equivalence tests are needed in the worst case to identify the equivalence classes with at least k members in set of n elements. The upper bound is an improvement by a factor 2 compared to known results. For k = 3 we give tighter bounds. Finally, for k > n/2 we prove that it is necessary and it suces to make 2n - k - 1 equivalence tests which generalizes a known result for k = ⌈(n+1)/2⌉. (Update)

Context of citations to this paper:   More

...is I r queries or BTO s. This can be shown to be very close to optimal using a worst case bound known for a related easier problem [2]. We use this result to generate supervision data for the algorithms described in Section 4.1 as follows: For algorithm (7) choose (at...

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BibTeX entry:   (Update)

P. G. Binderup, G. S. Frandsen, P. Bro Miltersen, and S. Skyum. The complexity of identifying large equivalence classes. qBRICS RS 98-34, University of Aarhus, DK, 1998. 20 http://citeseer.ist.psu.edu/binderup98complexity.html   More

@techreport{ binderup98complexity,
  author = "P. Binderup and G. Frandsen and P. Miltersen and S. Skyum",
  title = "The complexity of identifying large equivalence classes",
  number = "RS 98--34", 
  institution = "BRICS, University of Aarhus, DK",
  year = "1998",
  url = "citeseer.ist.psu.edu/binderup98complexity.html" }
Citations (may not include all citations):
193   Extremal Graph Theory (context) - Bollob - 1978
24   A Note on Ramsey Numbers (context) - Ajtai, omlos et al. - 1980
23   Science of Computer Programming (context) - Misra, Gries et al. - 1982
11   On Computing Majority by Comparisons (context) - Saks, Werman - 1991
7   Information Processing Letters (context) - Alonso, Reingold et al. - 1993
5   Solution to problem (context) - Fischer, Salzburg - 1982
5   An Optimal Algorithm for the Majority Problem (context) - Matula - 1990
4   Journal of Algorithms (context) - Moore - 1981
3   Finding a Majority when Sorting is not available (context) - Campbell, McNeill - 1991
2   The Complexity of Finding Replicas using Equality Tests - Frandsen, Miltersen et al. - 1993
2   London Mathematical Society Lecture Note Series 123 (context) - Graham, odl et al. - 1987
1   A Combinatorial Problem (context) - Binderup - 1998

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