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

Tetsuo Asano, Tomomi Matsui, Takeshi Tokuyama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationAlgorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings
EditorsMagnús M. Halldórsson
Number of pages14
ISBN (Print)3540676902, 9783540676904
Publication statusPublished - 2000 Jan 1
Event7th Scandinavian Workshop on Algorithm Theory, SWAT 2000 - Bergen, Norway
Duration: 2000 Jul 52000 Jul 7

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other7th Scandinavian Workshop on Algorithm Theory, SWAT 2000

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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