## Abstract

In this paper we study the problem of rounding a real-valued matrix into an integer-valued matrix to rmmmize an L_{p}-discrepancy measure between them. To define the L_{p}-discrepancy measure, we introduce a family F of regions (rigid submatrices) of the matrix, and consider a hypergraph defined by the family. The difficulty of the problem depends on the choice of the region family J-. We first investigate the rounding problem by using integer programming problems with convex piecewise-linear objective functions, and give some nontrivial upper bounds for the L_{p}-discrepancy. Then, we propose "laminar family" for constructing a practical and well-solvable class of T. Indeed, we show that the problem is solvable in polynomial time if T is a union of two laminar families. Finally, we show that the matrix rounding using Li-discrepancy for a union of two laminar families is suitable for developing a high-quality digital-halftoning software.

Original language | English |
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Title of host publication | Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002 |

Publisher | Association for Computing Machinery |

Pages | 896-904 |

Number of pages | 9 |

ISBN (Electronic) | 089871513X |

Publication status | Published - 2002 Jan 1 |

Event | 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002 - San Francisco, United States Duration: 2002 Jan 6 → 2002 Jan 8 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | 06-08-January-2002 |

### Other

Other | 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002 |
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Country/Territory | United States |

City | San Francisco |

Period | 02/1/6 → 02/1/8 |

## ASJC Scopus subject areas

- Software
- Mathematics(all)

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