On the complexities of the optimal rounding problems of sequences and matrices

Tetsuo Asano, Tomomi Matsui, Takeshi Tokuyama

研究成果: Conference contribution

7 被引用数 (Scopus)

抄録

In this paper, we discuss the problem of computing an opti-mal rounding of a real sequence (resp. matrix) into an integral sequence (resp. matrix). Our criterion of the optimality is to minimize the weighted l distance DistF,w (A;B) between an input sequence (resp. matrix) A and the output B. The distance is dependent on a family F of inter-vals (resp. rectangular regions) for the sequence rounding (resp. matrix rounding) and positive valued weight function w on the family. We give efficient polynomial time algorithms for the sequence-rounding problem, one for the weighted l1 distance, and the other for any weight function w, for any family F of intervals. We give an algorithm that computes a ma-trix rounding with an error at most 1:75 with respect to the unweighted l distance associated with the family W2 of all 2 × 2 square regions, whereas we prove that it is NP-hard to compute an approximate solution to the matrix-rounding problem with an approximate ratio smaller than 2 for the same distance.

本文言語English
ホスト出版物のタイトルAlgorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings
編集者Magnús M. Halldórsson
出版社Springer-Verlag
ページ476-489
ページ数14
ISBN(印刷版)3540676902, 9783540676904
DOI
出版ステータスPublished - 2000 1 1
イベント7th Scandinavian Workshop on Algorithm Theory, SWAT 2000 - Bergen, Norway
継続期間: 2000 7 52000 7 7

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
1851
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

Other7th Scandinavian Workshop on Algorithm Theory, SWAT 2000
国/地域Norway
CityBergen
Period00/7/500/7/7

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

フィンガープリント

「On the complexities of the optimal rounding problems of sequences and matrices」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル