Cache-oblivious comparison-based algorithms on multisets

Authors:
Arash Farzan;Paolo Ferragina;Gianni Franceschini;J. Ian Munro
Affiliations:
School of Computer Science, University of Waterloo;Department of Computer Science, University of Pisa;Department of Computer Science, University of Pisa;School of Computer Science, University of Waterloo
Venue:
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Year:
2005

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Abstract

We study three comparison-based problems related to multisets in the cache-oblivious model: Duplicate elimination, multisorting and finding the most frequent element (the mode). We are interested in minimizing the cache complexity (or number of cache misses) of algorithms for these problems in the context under which cache size and block size are unknown. We give algorithms with cache complexities within a constant factor of the optimal for all the problems. In the case of determining the mode, the optimal algorithm is randomized as the deterministic algorithm differs from the lower bound by a sublogarithmic factor. We can achieve optimality either with a randomized method or if given, along with the input, lg lg of relative frequency of the mode with a constant additive error.