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Summary: I/O-Space Trade-O s
(Extended Abstract)
Lars Arge ?1 and Jakob Pagter ??2
1 Department of Computer Science, Duke University, Durham, NC 27708, USA
2 BRICS ? ? ? , University of Aarhus, DK-8000 Aarhus C, Denmark
Abstract. We de ne external memory (or I/O) models which capture
space complexity and develop a general technique for deriving I/O-space
trade-o s in these models from internal memory model time-space trade-
o s. Using this technique we show strong I/O-space product lower bounds
for Sorting and Element Distinctness. We also develop new space
eÆcient external memory Sorting algorithms.
1 Introduction
In internal memory models the time and space complexity, as well as trade-o s
between the two, are well studied for fundamental problems such as Sorting
and Element Distinctness. For example, Pagter and Rauhe [20] recently
proved an O(N 2 ) upper bound on the time-space product for Sorting N ele-
ments, matching a lower bound of Beame [9]. Their algorithm can be used to
improve space usage of time-optimal internal memory Sorting by a factor of
(log 2 N) compared to classical algorithms like MergeSort and HeapSort.
Such an improvement would be of considerable practical interest when dealing
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