On the limits of cache-obliviousness

  • Authors:
  • Gerth Stølting Brodal;Rolf Fagerberg

  • Affiliations:
  • University of Aarhus, Ny Munkegade, Aarhus C, Denmark;University of Aarhus, Ny Munkegade, Aarhus C, Denmark

  • Venue:
  • Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
  • Year:
  • 2003

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Abstract

In this paper, we present lower bounds for permuting and sorting in the cache-oblivious model. We prove that (1) I/O optimal cache-oblivious comparison based sorting is not possible without a tall cache assumption, and (2) there does not exist an I/O optimal cache-oblivious algorithm for permuting, not even in the presence of a tall cache assumption.Our results for sorting show the existence of an inherent trade-off in the cache-oblivious model between the strength of the tall cache assumption and the overhead for the case M » B, and show that Funnelsort and recursive binary mergesort are optimal algorithms in the sense that they attain this trade-off.