The structure and number of global roundings of a graph

Tetsuo Asano, Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Given a connected weighted graph G = (V, E), we consider a hypergraph HG = (V, PG) corresponding to the set of all shortest paths in G. For a given real assignment a on V satisfying 0 ≤ a(υ) ≤ 1, a global rounding a with respect to HG is a binary assignment satisfying that |∑υ∈F a(υ) - α(υ)| < 1 for every F ∈ PG. 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)130-138
Number of pages9
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publication statusPublished - 2003

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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