The combinatorial encoding of disjoint convex sets in the plane

We introduce a new combinatorial object, the double-permutation sequence, and use it to encode a family of mutually disjoint compact convex sets in the plane in a way that captures many of its combinatorial properties. We use this encoding to give a new proof of the Edelsbrunner-Sharir theorem that a collection of n compact convex sets in the plane cannot be met by straight lines in more than 2n

• Type: Journal
• Year: 2008
• Where: COMBINATORICA
• Authors: Jacob E. Goodman, Richard Pollack
• Keywords: COMBINATORICA 2008, Compact Connected Sets, Compact Convex, Disjoint Compact Convex