On geometric structure of global roundings for graphs and range spaces

Tetsuo Asano, Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

Given a hypergraph H = (V, ℱ) and a [0, 1]-valued vector a ∈ [0,1]V, its global rounding is a binary (i.e.,{0, 1}-valued) vector α ∈ {0,1}V such that |∑υ∈F (a(υ)-α(υ))| < 1 holds fo each F ε ℱ. We study geometric (or combinatorial) structure of the set of global roundings of a using the notion of compatible set with respect to the discrepancy distance. We conjecture that the set of global roundings forms a simplex if the hypergraph satisfies "shortest-path" axioms, and prove it for some special cases including some geometric range spaces and the shortest path hypergraph of a series-parallel graph.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsTorben Hagerup, Jyrki Katajainen
PublisherSpringer Verlag
Pages455-467
Number of pages13
ISBN (Electronic)3540223398, 9783540223399
DOIs
Publication statusPublished - 2004 Jan 1

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3111
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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