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 |Σv∈F a(v) − α(v)| < 1 for every F ∈ P G. We conjecture that there are at most |V| + 1 global roundings for H G, and also the set of global roundings is an affine independent set. We give several positive evidences for the conjecture.
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Asano, T., Katoh, N., Tamaki, H., Tokuyama, T. (2003). The Structure and Number of Global Roundings of a Graph. In: Warnow, T., Zhu, B. (eds) Computing and Combinatorics. COCOON 2003. Lecture Notes in Computer Science, vol 2697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45071-8_15
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DOI: https://doi.org/10.1007/3-540-45071-8_15
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