 
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. 106114, Springer Verlag
1
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
