TY - CHAP

T1 - On geometric structure of global roundings for graphs and range spaces

AU - Asano, Tetsuo

AU - Katoh, Naoki

AU - Tamaki, Hisao

AU - Tokuyama, Takeshi

PY - 2004/1/1

Y1 - 2004/1/1

N2 - 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 |∑υ∈F (a(υ)-α(υ))| < 1 holds fo each F ε 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 special cases including some geometric range spaces and the shortest path hypergraph of a series-parallel graph.

AB - 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 |∑υ∈F (a(υ)-α(υ))| < 1 holds fo each F ε 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 special cases including some geometric range spaces and the shortest path hypergraph of a series-parallel graph.

UR - http://www.scopus.com/inward/record.url?scp=35048871137&partnerID=8YFLogxK

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U2 - 10.1007/978-3-540-27810-8_39

DO - 10.1007/978-3-540-27810-8_39

M3 - Chapter

AN - SCOPUS:35048871137

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 455

EP - 467

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Hagerup, Torben

A2 - Katajainen, Jyrki

PB - Springer Verlag

ER -