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Shortcuts for the Circle

Let C be the unit circle in R^2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k >= 1 shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1 <= k...

Placing your Coins on a Shelf

thank all participants at the Korean Workshop on Computational Geometry in W?rzburg 2016. 1 2 3 4 5 6 7 8 9 10 11 Helmut Alt , Kevin Buchin, Steven Chaplick, Otfried Cheong, Philipp Kindermann

Approximating Convex Shapes With Respect to Symmetric Difference Under Homotheties

The symmetric difference is a robust operator for measuring the error of approximating one shape by another. Given two convex shapes P and C, we study the problem of minimizing the volume of their symmetric difference under all possible scalings and translations of C. We prove that the problem can be solved by convex programming. We also present a combinatorial algorithm for...

Finding a Guard that Sees Most and a Shop that Sells Most

Discrete Comput Geom Geometry Discrete & Computational Otfried Cheong 2 Alon Efrat 1 Sariel Har-Peled 0 0 Department of Computer Science, University of Illinois , 201 N. Goodwin Avenue, Urbana ... of intersection of two polygonal regions in near-quadratic time, and the rigid motion doing so in near-cubic time. ∗ Work on this paper by Otfried Cheong was supported by the Brain Korea 21 Project