The structure and number of global roundings of a graph

Authors:
Tetsuo Asano;Naoki Katoh;Hisao Tamaki;Takeshi Tokuyama
Affiliations:
School of Information Science, Japan Advanced Institute of Science and Technology, Tatsunokuchi, Japan;Graduate School of Engineering, Kyoto University, Kyoto, Japan;Meiji University, Kawasaki, Japan;GSIS, Tohoku University, Sendai, Japan
Venue:
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Year:
2003

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Abstract

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 | Σv∈F - a(v)-α(v)| 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.