### Abstract

Original language | English |
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Title of host publication | Algorithms and Computation, 20th International ymposium, ISAAC |

Volume | 5878 |

Publisher | Springer |

Publication date | 2009 |

Pages | 173-182 |

DOIs | |

Publication status | Published - 2009 |

Event | Algorithms and Computation - Duration: 24. Aug 2010 → … Conference number: 20 |

### Conference

Conference | Algorithms and Computation |
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Number | 20 |

Period | 24/08/2010 → … |

Series | Lecture Notes in Computer Science |
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Volume | 5878 |

### Fingerprint

### Cite this

*Algorithms and Computation, 20th International ymposium, ISAAC*(Vol. 5878, pp. 173-182). Springer. Lecture Notes in Computer Science, Vol.. 5878 https://doi.org/10.1007/978-3-642-10631-6_19

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*Algorithms and Computation, 20th International ymposium, ISAAC.*vol. 5878, Springer, Lecture Notes in Computer Science, vol. 5878, pp. 173-182, Algorithms and Computation, 24/08/2010. https://doi.org/10.1007/978-3-642-10631-6_19

**Online Sorted Range Reporting.** / Brodal, Gerth Stølting; Fagerberg, Rolf; Greve, Mark; López-Ortiz, Alejandro.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - Online Sorted Range Reporting

AU - Brodal, Gerth Stølting

AU - Fagerberg, Rolf

AU - Greve, Mark

AU - López-Ortiz, Alejandro

PY - 2009

Y1 - 2009

N2 - We study the following one-dimensional range reporting problem: On an array A of n elements, support queries that given two indices i ≤ j and an integer k report the k smallest elements in the subarray A[i..j] in sorted order. We present a data structure in the RAM model supporting such queries in optimal O(k) time. The structure uses O(n) words of space and can be constructed in O(n logn) time. The data structure can be extended to solve the online version of the problem, where the elements in A[i..j] are reported one-by-one in sorted order, in O(1) worst-case time per element. The problem is motivated by (and is a generalization of) a problem with applications in search engines: On a tree where leaves have associated rank values, report the highest ranked leaves in a given subtree. Finally, the problem studied generalizes the classic range minimum query (RMQ) problem on arrays.

AB - We study the following one-dimensional range reporting problem: On an array A of n elements, support queries that given two indices i ≤ j and an integer k report the k smallest elements in the subarray A[i..j] in sorted order. We present a data structure in the RAM model supporting such queries in optimal O(k) time. The structure uses O(n) words of space and can be constructed in O(n logn) time. The data structure can be extended to solve the online version of the problem, where the elements in A[i..j] are reported one-by-one in sorted order, in O(1) worst-case time per element. The problem is motivated by (and is a generalization of) a problem with applications in search engines: On a tree where leaves have associated rank values, report the highest ranked leaves in a given subtree. Finally, the problem studied generalizes the classic range minimum query (RMQ) problem on arrays.

U2 - 10.1007/978-3-642-10631-6_19

DO - 10.1007/978-3-642-10631-6_19

M3 - Article in proceedings

VL - 5878

T3 - Lecture Notes in Computer Science

SP - 173

EP - 182

BT - Algorithms and Computation, 20th International ymposium, ISAAC

PB - Springer

ER -