The structure and number of global roundings of a graph

Tetsuo Asano, Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama

Research output: Contribution to journalConference articlepeer-review

3 Citations (Scopus)

Abstract

Given a connected weighted graph G = (V, E), we consider a hypergraph HG = (V, script P sign G) corresponding to the set of all shortest paths in G. For a given real assignment a on V satisfying 0≤a(v)≤1, a global rounding a with respect to HG is a binary assignment satisfying that |Σu∈Fa(v) - α(v)| - < 1 for every F ∈ script P sign G. We conjecture that there are at most |V| + 1 global roundings for HG, and also the set of global roundings is an affine independent set. We give several positive evidences for the conjecture.

Original languageEnglish
Pages (from-to)425-437
Number of pages13
JournalTheoretical Computer Science
Volume325
Issue number3
DOIs
Publication statusPublished - 2004 Oct 6
EventSelected Papers from COCOON 2003 - Big Sky, United States
Duration: 2003 Jul 252003 Jul 28

Keywords

  • Combinatorics
  • Discrepancy
  • Graph
  • Hypergraph
  • Rounding

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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