TY - GEN

T1 - How to cut pseudo-parabolas into segments

AU - Tamaki, Hisao

AU - Tokuyama, Takeshi

N1 - Publisher Copyright:
© 1995 ACM.

PY - 1995/9/1

Y1 - 1995/9/1

N2 - Let Γ be a collection of unbounded x-monotone Jordan arcs intersecting at most twice each other, which we call pseudo-parabolas, since two axis parallel parabolas intersects at most twice. We investigate how to cut pseudo-parabolas into the minimum number of curve segments so that each pair of segments intersect at most once. We give an Ω(n4/3) lower bound and O(n5/3) upper bound. We give the same bounds for an arrangement of circles. Applying the upper bound, we give an O(n23/12) bound on the complexity of a level of pseudo-parabolas, and O(n11/6) bound on the complexity of a combinatorially concave chain of pseudo parabolas. We also give some upperbounds on the number of transitions of the minimum weight matroid base when the weight of each element changes as a quadratic function of a single parameter.

AB - Let Γ be a collection of unbounded x-monotone Jordan arcs intersecting at most twice each other, which we call pseudo-parabolas, since two axis parallel parabolas intersects at most twice. We investigate how to cut pseudo-parabolas into the minimum number of curve segments so that each pair of segments intersect at most once. We give an Ω(n4/3) lower bound and O(n5/3) upper bound. We give the same bounds for an arrangement of circles. Applying the upper bound, we give an O(n23/12) bound on the complexity of a level of pseudo-parabolas, and O(n11/6) bound on the complexity of a combinatorially concave chain of pseudo parabolas. We also give some upperbounds on the number of transitions of the minimum weight matroid base when the weight of each element changes as a quadratic function of a single parameter.

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U2 - 10.1145/220279.220304

DO - 10.1145/220279.220304

M3 - Conference contribution

AN - SCOPUS:0039226321

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 230

EP - 237

BT - Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995

PB - Association for Computing Machinery

T2 - 11th Annual Symposium on Computational Geometry, SCG 1995

Y2 - 5 June 1995 through 7 June 1995

ER -