On the limits of cache-obliviousness

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. Categories and Subject Descriptors

• Type: Conference
• Year: 2003
• Where: STOC
• Authors: Gerth Stølting Brodal, Rolf Fagerberg
• Keywords: Algorithms, Cache-oblivious Model, Recursive Binary Mergesort, STOC 2003, Tall Cache Assumption