### Abstract

A large class of geometric retrieval problems has the following form. Given a set X of geometric objects, preprocess to obtain a data structure D(X). Now use D(X) to rapidly answer queries on X. We say an algorithm for such a problem has (worst-case) space-time complexity O(f(n), g(n)) if the space requirement for D(X) is O(f) and the "locate run-time" required for each retrieval is O(g). We show three techniques which can consistently be exploited in solving such problems. For instance, using our techniques, we obtain an O(n^{2 + ε}/log n, log n log(1/ε)) space-time algorithm for the polygon retrieval problem, for arbitrarily small ε, improving on the previous solution having complexity O(n^{7}, log n).

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

Pages (from-to) | 39-57 |

Number of pages | 19 |

Journal | Information and control |

Volume | 63 |

Issue number | 1-2 |

DOIs | |

State | Published - 1984 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Information and control*,

*63*(1-2), 39-57. https://doi.org/10.1016/S0019-9958(84)80040-6

**Geometric retrieval problems.** / Cole, Richard; Yap, Chee.

Research output: Contribution to journal › Article

*Information and control*, vol. 63, no. 1-2, pp. 39-57. https://doi.org/10.1016/S0019-9958(84)80040-6

}

TY - JOUR

T1 - Geometric retrieval problems

AU - Cole, Richard

AU - Yap, Chee

PY - 1984

Y1 - 1984

N2 - A large class of geometric retrieval problems has the following form. Given a set X of geometric objects, preprocess to obtain a data structure D(X). Now use D(X) to rapidly answer queries on X. We say an algorithm for such a problem has (worst-case) space-time complexity O(f(n), g(n)) if the space requirement for D(X) is O(f) and the "locate run-time" required for each retrieval is O(g). We show three techniques which can consistently be exploited in solving such problems. For instance, using our techniques, we obtain an O(n2 + ε/log n, log n log(1/ε)) space-time algorithm for the polygon retrieval problem, for arbitrarily small ε, improving on the previous solution having complexity O(n7, log n).

AB - A large class of geometric retrieval problems has the following form. Given a set X of geometric objects, preprocess to obtain a data structure D(X). Now use D(X) to rapidly answer queries on X. We say an algorithm for such a problem has (worst-case) space-time complexity O(f(n), g(n)) if the space requirement for D(X) is O(f) and the "locate run-time" required for each retrieval is O(g). We show three techniques which can consistently be exploited in solving such problems. For instance, using our techniques, we obtain an O(n2 + ε/log n, log n log(1/ε)) space-time algorithm for the polygon retrieval problem, for arbitrarily small ε, improving on the previous solution having complexity O(n7, log n).

UR - http://www.scopus.com/inward/record.url?scp=0021503111&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021503111&partnerID=8YFLogxK

U2 - 10.1016/S0019-9958(84)80040-6

DO - 10.1016/S0019-9958(84)80040-6

M3 - Article

VL - 63

SP - 39

EP - 57

JO - Information and Computation

JF - Information and Computation

SN - 0890-5401

IS - 1-2

ER -