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Mulzer, Wolfgang; Phillips, Jeff M (Ed.)We propose precise notions of what it means to guard a domain "robustly", under a variety of models. While approximation algorithms for minimizing the number of (precise) point guards in a polygon is a notoriously challenging area of investigation, we show that imposing various degrees of robustness on the notion of visibility coverage leads to a more tractable (and realistic) problem for which we can provide approximation algorithms with constant factor guarantees.more » « less
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Mavronicolas, Marios (Ed.)Let {\$$}{\$$}E={\backslash}{\{}e{\_}1,{\backslash}ldots ,e{\_}n{\backslash}{\}}{\$$}{\$$}be a set of C-oriented disjoint segments in the plane, where C is a given finite set of orientations that spans the plane, and let s and t be two points. We seek a minimum-link C-oriented tour of E, that is, a polygonal path {\$$}{\$$}{\backslash}pi {\$$}{\$$}from s to t that visits the segments of E in order, such that, the orientations of its edges are in C and their number is minimum. We present an algorithm for computing such a tour in {\$$}{\$$}O(|C|^2 {\backslash}cdot n^2){\$$}{\$$}time. This problem already captures most of the difficulties occurring in the study of the more general problem, in which E is a set of not-necessarily-disjoint C-oriented polygons.more » « less
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We give an overview of the 2021 Computational Geometry Challenge, which targeted the problem of optimally coordinating a set of robots by computing a family of collision-free trajectories for a set S of n pixel-shaped objects from a given start configuration to a desired target configuration.more » « less
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We give an overview of theoretical and practical aspects of finding a simple polygon of minimum ( Min-Area ) or maximum ( Max-Area ) possible area for a given set of n points in the plane. Both problems are known to be NP -hard and were the subject of the 2019 Computational Geometry Challenge, which presented the quest of finding good solutions to more than 200 instances, ranging from n = 10 all the way to n = 1, 000, 000.more » « less
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