A model for hierarchical memory
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The input/output complexity of sorting and related problems
Communications of the ACM
External memory algorithms and data structures: dealing with massive data
ACM Computing Surveys (CSUR)
On the limits of cache-obliviousness
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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Intuitively, a cache-oblivious algorithm implements an adaptive strategy which runs efficiently on any memory hierarchy without requiring previous knowledge of the parameters of the hierarchy. For this reason, cache-obliviousness is an attractive feature of an algorithm meant for a global computing environment, where software may be run on a variety of different platforms for load management purposes. In this paper we present a negative result on cache-obliviousness, namely, we show that an optimal cache-oblivious algorithm for the fundamental primitive of matrix transposition cannot exist without the tall cache assumption, which forces the (unknown) parameters of the memory hierarchy to satisfy a certain technical relation. Our contribution specializes the result of Brodal and Fagerberg for general permutations to matrix transposition, and provides further evidence that the tall cache assumption is often necessary to attain optimality in the context of cache-oblivious algorithms.