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(v) ≤ 1, a global rounding α with respect to Hg is a binary assignment satisfying that |∑_(v∈F)a(v)-α(v)| < 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.
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机译：给定连接的加权图G =（v，e），我们考虑与G的所有最短路径集对应的超图HG =（v，pg）。对于在v满意0≤a（v）上的给定实际分配a ≤1，相对于HG的全局圆形α是满足其的二进制分配|Σ_（v∈f）a（v）-α（v）| <1对于每个f∈PG。我们猜想最多有| v | + 1用于HG的全球圆角，而且全球圆角的集合是一个仿射独立集。我们为猜想提供了几个积极的证据。
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