Transversals and Epsilon Nets
Here we are going to consider problems of the following type: We have a family F of geometric shapes satisfying certain conditions, and we would like to conclude that F can be “pierced” by not too many points, meaning that we can choose a bounded number of points such that each set of F contains at least one of them. Such questions are sometimes called Gallai-type problems, because of the following nice problem raised by Gallai: Let F be a finite family of closed disks in the plane such that every two disks in F intersect. What is the smallest number of points needed to pierce F For this problem, the exact answer is known: 4 points always suffice and are sometimes necessary.
KeywordsFractional Packing Finite Family Line Transversal Common Tangent Helly Number
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