### Abstract

Given string S[1⋯N] and integer k, the suffix selection problem is to determine the kth lexicographically smallest amongst the suffixes S[i ⋯ N], 1 ≤ i ≤ N. We study the suffix selection problem in the cache-aware model that captures two-level memory inherent in computing systems, for a 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 θ (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 = Ω (B^{1+∈}), where ∈ < 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.

Original language | English (US) |
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Title of host publication | STACS 2009 - 26th International Symposium on Theoretical Aspects of Computer Science |

Pages | 457-468 |

Number of pages | 12 |

State | Published - Dec 1 2009 |

Event | 26th International Symposium on Theoretical Aspects of Computer Science, STACS 2009 - Freiburg, Germany Duration: Feb 26 2009 → Feb 28 2009 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 3 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 26th International Symposium on Theoretical Aspects of Computer Science, STACS 2009 |
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Country | Germany |

City | Freiburg |

Period | 2/26/09 → 2/28/09 |

### Fingerprint

### ASJC Scopus subject areas

- Software

### Cite this

*STACS 2009 - 26th International Symposium on Theoretical Aspects of Computer Science*(pp. 457-468). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 3).

**Optimal cache-aware suffix selection.** / Franceschini, Gianni; Grossi, Roberto; Muthukrishnan, Shanmugavelayutham.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*STACS 2009 - 26th International Symposium on Theoretical Aspects of Computer Science.*Leibniz International Proceedings in Informatics, LIPIcs, vol. 3, pp. 457-468, 26th International Symposium on Theoretical Aspects of Computer Science, STACS 2009, Freiburg, Germany, 2/26/09.

}

TY - GEN

T1 - Optimal cache-aware suffix selection

AU - Franceschini, Gianni

AU - Grossi, Roberto

AU - Muthukrishnan, Shanmugavelayutham

PY - 2009/12/1

Y1 - 2009/12/1

N2 - Given string S[1⋯N] and integer k, the suffix selection problem is to determine the kth lexicographically smallest amongst the suffixes S[i ⋯ N], 1 ≤ i ≤ N. We study the suffix selection problem in the cache-aware model that captures two-level memory inherent in computing systems, for a 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 θ (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 = Ω (B1+∈), where ∈ < 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.

AB - Given string S[1⋯N] and integer k, the suffix selection problem is to determine the kth lexicographically smallest amongst the suffixes S[i ⋯ N], 1 ≤ i ≤ N. We study the suffix selection problem in the cache-aware model that captures two-level memory inherent in computing systems, for a 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 θ (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 = Ω (B1+∈), where ∈ < 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.

UR - http://www.scopus.com/inward/record.url?scp=84880233134&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880233134&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84880233134

SN - 9783939897095

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 457

EP - 468

BT - STACS 2009 - 26th International Symposium on Theoretical Aspects of Computer Science

ER -