Enumerating global roundings of an outerplanar graph

Nadia Takki-Chebihi, Takeshi Tokuyama

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

Given a connected weighted graph G = (V, E), we consider a hypergraph H G = (V, P 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 α with respect to H G is a binary assignment satisfying that |∑ v∈Fa(v)-α(v)| < 1 for every F ∈ P G. Asano et al [1] conjectured that there are at most |V|+1 global roundings for H G. In this paper, we prove that the conjecture holds if G is an outerplanar graph. Moreover, we give a polynomial time algorithm for enumerating all the global roundings of an outerplanar graph.

Original languageEnglish
Pages (from-to)425-433
Number of pages9
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2906
Publication statusPublished - 2003 Dec 1

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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