 
Summary: DIMACS Series in Discrete Mathematics
and Theoretical Computer Science
On Showing Lower Bounds for ExternalMemory
Computational Geometry Problems
Lars Arge and Peter Bro Miltersen
Abstract. In this paper we consider lower bounds for externalmemory com
putational geometry problems. We find that it is not quite clear which model
of computation to use when considering such problems. As an attempt of pro
viding a model, we define the external memory Turing machine model, and we
derive lower bounds for a number of problems, including the element distinct
ness problem. For these lower bounds we make the standard assumption that
records are indivisible. Waiving the indivisibility assumption we show how to
beat the lower bound for element distinctness. As an alternative model, we
briefly discuss an externalmemory version of the algebraic computation tree.
1. Introduction
The Input/Output (or just I/O) communication between fast internal memory
and slower external storage is the bottleneck in many largescale computations.
The significance of this bottleneck is increasing as internal computation gets faster,
and as parallel computation gains popularity. Currently, technological advances
are increasing CPU speeds at an annual rate of 4060% while disk transfer rates
