Structure Theorems for Systems of Segments

Authors:
János Pach;József Solymosi
Affiliations:
-;-
Venue:
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Year:
2000

Citing 7
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Abstract

We study intersection properties of systems of segments in the plane. In particular, we show that there exists a constant c 0 such that every system S of n straight-line segments in the plane has two at least cn-element subsystems S1, S2 驴 S such that either every segment in S1 intersects all elements of S2, or no segment in S1 intersects any element of S2. We also propose a fast approximate solution for reporting most intersections among n segments in the plane.