Combinatorics and algorithms on low-discrepancy roundings of a real sequence

Kunihiko Sadakane, Nadia Takki-Chebihi, Takeshi Tokuyama

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

17 Citations (Scopus)

Abstract

In this paper, we discuss the problem of computing all the integral sequences obtained by rounding an input real valued sequence such that the discrepancy between the input sequence and each output integral sequence is less than one. We show that the number of such roundings is n + 1 if we consider the discrepancy with respect to the set of all subintervals, and give an effcient algorithm to report all of them. Then, we give an optimal method to construct a compact graph to represent the set of global roundings satisfying a weaker discrepancy condition.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings
EditorsFernando Orejas, Paul G. Spirakis, Jan van Leeuwen
PublisherSpringer Verlag
Pages166-177
Number of pages12
ISBN (Print)3540422870, 9783540422877
DOIs
Publication statusPublished - 2001 Jan 1
Event28th International Colloquium on Automata, Languages and Programming, ICALP 2001 - Crete, Greece
Duration: 2001 Jul 82001 Jul 12

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2076 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other28th International Colloquium on Automata, Languages and Programming, ICALP 2001
CountryGreece
CityCrete
Period01/7/801/7/12

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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