Optimal cache-aware suffix selection

Abstract : Given string $S[1..N]$ and integer $k$, the {\em suffix selection} problem is to determine the $k$th lexicographically smallest amongst the suffixes $S[i\ldots N]$, $1 \leq i \leq N$. We study the suffix selection problem in the cache-aware model that captures two-level memory inherent in computing systems, for a \emph{cache} of limited size $M$ and block size $B$. The complexity of interest is the number of block transfers. We present an optimal suffix selection algorithm in the cache-aware model, requiring $\Thetah{N/B}$ block transfers, for any string $S$ over an unbounded alphabet (where characters can only be compared), under the common tall-cache assumption (i.e. $M=\Omegah{B^{1+\epsilon}}$, where $\epsilon<1$). Our algorithm beats the bottleneck bound for permuting an input array to the desired output array, which holds for nearly any nontrivial problem in hierarchical memory models.
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Submitted on : Tuesday, February 10, 2009 - 5:20:02 PM
Last modification on : Tuesday, February 26, 2019 - 10:54:02 AM
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• HAL Id : inria-00359742, version 1
• ARXIV : 0902.1737

Citation

Gianni Franceschini, Roberto Grossi, S. Muthukrishnan. Optimal cache-aware suffix selection. 26th International Symposium on Theoretical Aspects of Computer Science - STACS 2009, Feb 2009, Freiburg, Germany. pp.457-468. ⟨inria-00359742⟩

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