The Structure and Number of Global Roundings of a Graph
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چکیده
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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تاریخ انتشار 2003