Summary: Tight Worst­Case Bounds on the Dictionary Problem \Lambda
Arne Andersson
Department of Computer Science
Lund University
Box 118
S ­ 221 00 Lund
Sweden
\Lambda A preliminary version published in Proceedings of International Symposium of Optimal Algorithms, 1989, Lecture
Notes in Computer Science 401, pp. 106--114, Springer Verlag
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Abstract
An improved worst­case bound on the dictionary problem in a comparison­based model of com­
putation is presented. Dictionary operation can be performed at a worst­case cost of O(log n),
using only dlog(n + 1) + ffle comparisons, where ffl is an arbitrary positive constant. We feel that
this fact leads to a deeper understanding of of this well­studied and fundamental problem.
We also give two applications. First, we improve the upper bound on on­line sorting: for
each value of ffi, ffi ? 0, there is a worst­case efficient on­line sorting algorithm using less than
P N
n=1 dlog ne+ ffiN +log N comparisons when sorting N elements. By worst­case efficient on­line

Source: Andersson, Arne - Department of Information Technology, Uppsala Universitet

Collections: Computer Technologies and Information Sciences