On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema
IEEE Transactions on Pattern Analysis and Machine Intelligence
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Survivable Networks: Algorithms for Diverse Routing
Survivable Networks: Algorithms for Diverse Routing
Translating a Planar Object to Maximize Point Containment
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
On Approximating the Depth and Related Problems
SIAM Journal on Computing
Topology Design of Undersea Cables Considering Survivability Under Major Disasters
WAINA '09 Proceedings of the 2009 International Conference on Advanced Information Networking and Applications Workshops
Network reliability with geographically correlated failures
INFOCOM'10 Proceedings of the 29th conference on Information communications
Relative (p,ε)-Approximations in Geometry
Discrete & Computational Geometry
Add isotropic Gaussian kernels at own risk: more and more resilient modes in higher dimensions
Proceedings of the twenty-eighth annual symposium on Computational geometry
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Let C=C1,...,Cn} be a set of n pairwise-disjoint convex s-gons, for some constant s, and let p be a probability density function (pdf) over the non-negative reals. For each i, let Ki be the Minkowski sum of Ci with a disk of radius ri, where each ri is a random non-negative number drawn independently from the distribution determined by π. We show that the expected complexity of the union of K1,..,Kn is O(n log n), for any pdf p; the constant of proportionality depends on s, but not on the pdf. Next, we consider the following problem that arises in analyzing the vulnerability of a network under a physical attack. Let G=(V,E) be a planar geometric graph where E is a set of n line segments with pairwise-disjoint relative interiors. Let f: R - [0,1] be an edge failure probability function, where a physical attack at a location x causes an edge e of E at distance r from x to fail with probability f(r); we assume that f is of the form f(x)=1-P(x), where P is a cumulative distribution function on the non-negative reals. The goal is to compute the most vulnerable location for G, i.e., the location of the attack that maximizes the expected number of failing edges of G. Using our bound on the complexity of the union of random Minkowski sums, we present a near-linear Monte-Carlo algorithm for computing a location that is an approximately most vulnerable location of attack for G.