 
Summary: A General Lower Bound on the I/OComplexity
of Comparisonbased Algorithms \Lambda
Lars Arge, Mikael Knudsen and Kirsten Larsen y
Aarhus University, Computer Science Department
Ny Munkegade, DK8000 Aarhus C. z
Abstract
We show a general relationship between the number of comparisons and the
number of I/Ooperations needed to solve a given problem. This relationship en
ables one to show lower bounds on the number of I/Ooperations needed to solve a
problem whenever a lower bound on the number of comparisons is known. We use
the result to show lower bounds on the I/Ocomplexity on a number of problems
where known techniques only give trivial bounds. Among these are the problems of
removing duplicates from a multiset, a problem of great importance in e.g. relational
database systems, and the problem of determining the mode the most frequently
occurring element of a multiset. We develop algorithms for these problems in order
to show that the lower bounds are tight.
1 Introduction
In the study of complexity of algorithms, most attention has been given to bounding the
number of primitive operations (for example comparisons) needed to solve a problem.
However, when working with data materials so large that they will not fit into internal
