## Abstract

In this paper, we investigate inverse problems of the interval query problem in application to data mining. Let I be the set of all intervals on U = {1, 2, . . . , n}. Consider an objective function f(I), conditional functions u_{i}(I) on I, and define an optimization problem of finding the interval I maximizing f(I) subject to u_{i}(I) > K_{i} for given real numbers K_{i} (i = 1, 2, . . . , h). We propose efficient algorithms to solve the above optimization problem if the objective function is either additive or quotient, and the conditional functions are additive, where a function f is additive if f(I) = ∑_{i∈I} f̂(i) extending a function f̂ on U, and quotient if it is represented as a quotient of two additive functions. We use computational-geometric methods such as convex hull, range searching, and multidimensional divide-and-conquer.

Original language | English |
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Pages (from-to) | 620-625 |

Number of pages | 6 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E80-A |

Issue number | 4 |

Publication status | Published - 1997 Jan 1 |

## Keywords

- Algorithms, data mining
- Computational geometry
- Interval searching

## ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics