On Geometric Structure of Global Roundings for Graphs and Range Spaces [chapter]

Tetsuo Asano, Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama
2004 Lecture Notes in Computer Science  
Given a hypergraph H = (V, F) and a [0, 1]-valued vector a ∈ [0, 1] V , its global rounding is a binary (i.e.,{0, 1}-valued) vector α ∈ {0, 1} V such that | v∈F (a(v)−α(v))| < 1 holds for each F ∈ F. We study geometric (or combinatorial) structure of the set of global roundings of a using the notion of compatible set with respect to the discrepancy distance. We conjecture that the set of global roundings forms a simplex if the hypergraph satisfies "shortest-path" axioms, and prove it for some
more » ... ecial cases including some geometric range spaces and the shortest path hypergraph of a series-parallel graph.
doi:10.1007/978-3-540-27810-8_39 fatcat:4dwa2ochwvdn3nrjshrjkmxhca