### Abstract

Given an array A[1,n] of elements with a total order,we consider the problem of building a data structure that solves two queries: a) selection queries receive a range [i,j] and an integer k and return the position of the kth largest element in A[i,j], b) top-k queries receive [i,j] and k and return the positions of the k largest elements in A[i,j]. These problems can be solved in optimal time,O(1 + lg k/lg lg n) and O(k),respectively,using linear-space data structures. We provide the first study of the encoding data structures for the above problems,where A cannot be accessed at query time. Several applications are interested in the relative order of the entries of A,and their positions,rather their actual values,and thus we do not need to keep A at query time. In those cases,encodings save storage space: we first show that any encoding answering such queries requires nlg k - O(n + klg k) bits of space,then,we design encodings using O(nlg k) bits,that is,asymptotically optimal up to constant factors,while preserving optimal query time.

Original language | English (US) |
---|---|

Article number | 28 |

Journal | ACM Transactions on Algorithms |

Volume | 13 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2017 |

### Fingerprint

### Keywords

- Encoding data structures
- Range minimum queries
- Range search data structures
- Succinct data structures

### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

*ACM Transactions on Algorithms*,

*13*(2), [28]. https://doi.org/10.1145/3012939

**Asymptotically optimal encodings of range data structures for selection and top-k queries.** / Grossi, Roberto; Iacono, John; Navarro, Gonzalo; Raman, Rajeev; Satti, S. Rao.

Research output: Contribution to journal › Article

*ACM Transactions on Algorithms*, vol. 13, no. 2, 28. https://doi.org/10.1145/3012939

}

TY - JOUR

T1 - Asymptotically optimal encodings of range data structures for selection and top-k queries

AU - Grossi, Roberto

AU - Iacono, John

AU - Navarro, Gonzalo

AU - Raman, Rajeev

AU - Satti, S. Rao

PY - 2017/3/1

Y1 - 2017/3/1

N2 - Given an array A[1,n] of elements with a total order,we consider the problem of building a data structure that solves two queries: a) selection queries receive a range [i,j] and an integer k and return the position of the kth largest element in A[i,j], b) top-k queries receive [i,j] and k and return the positions of the k largest elements in A[i,j]. These problems can be solved in optimal time,O(1 + lg k/lg lg n) and O(k),respectively,using linear-space data structures. We provide the first study of the encoding data structures for the above problems,where A cannot be accessed at query time. Several applications are interested in the relative order of the entries of A,and their positions,rather their actual values,and thus we do not need to keep A at query time. In those cases,encodings save storage space: we first show that any encoding answering such queries requires nlg k - O(n + klg k) bits of space,then,we design encodings using O(nlg k) bits,that is,asymptotically optimal up to constant factors,while preserving optimal query time.

AB - Given an array A[1,n] of elements with a total order,we consider the problem of building a data structure that solves two queries: a) selection queries receive a range [i,j] and an integer k and return the position of the kth largest element in A[i,j], b) top-k queries receive [i,j] and k and return the positions of the k largest elements in A[i,j]. These problems can be solved in optimal time,O(1 + lg k/lg lg n) and O(k),respectively,using linear-space data structures. We provide the first study of the encoding data structures for the above problems,where A cannot be accessed at query time. Several applications are interested in the relative order of the entries of A,and their positions,rather their actual values,and thus we do not need to keep A at query time. In those cases,encodings save storage space: we first show that any encoding answering such queries requires nlg k - O(n + klg k) bits of space,then,we design encodings using O(nlg k) bits,that is,asymptotically optimal up to constant factors,while preserving optimal query time.

KW - Encoding data structures

KW - Range minimum queries

KW - Range search data structures

KW - Succinct data structures

UR - http://www.scopus.com/inward/record.url?scp=85017109865&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017109865&partnerID=8YFLogxK

U2 - 10.1145/3012939

DO - 10.1145/3012939

M3 - Article

AN - SCOPUS:85017109865

VL - 13

JO - ACM Transactions on Algorithms

JF - ACM Transactions on Algorithms

SN - 1549-6325

IS - 2

M1 - 28

ER -