Abstract
Given a connected weighted graph G = (V, E), we consider a hypergraph \(\mathcal{H}_G = (V,\mathcal{P}_G)\) 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 \(\mathcal{H}_G\) is a binary assignment satisfying that | ∑ v ∈ F a(v) − α(v)| < 1 for every \(F \in \mathcal{P}_G\). Asano et al [1] conjectured that there are at most |V|+1 global roundings for \(\mathcal{H}_G\). 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.
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Takki-Chebihi, N., Tokuyama, T. (2003). Enumerating Global Roundings of an Outerplanar Graph. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_44
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DOI: https://doi.org/10.1007/978-3-540-24587-2_44
Publisher Name: Springer, Berlin, Heidelberg
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