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4 papers · 2 filters
A Center Transversal Theorem for Hyperplanes and Applications to Graph Drawing
Vida Dujmovic, Stefan Langerman
Motivated by an open problem from graph drawing, we study several partitioning problems for line and hyperplane arrangements. We prove a ham-sandwich cut theorem: given two sets of…
Minimum-Area Enclosing Triangle with a Fixed Angle
Prosenjit Bose, Jean-Lou De Carufel
Given a set S of n points in the plane and a fixed angle 0 < omega < pi, we show how to find in O(n log n) time all triangles of minimum area with one angle omega that enclose S. W…
Pi/2-Angle Yao Graphs are Spanners
Prosenjit Bose, Mirela Damian, Karim Douieb +4
We show that the Yao graph Y4 in the L2 metric is a spanner with stretch factor 8(29+23sqrt(2)). Enroute to this, we also show that the Yao graph Y4 in the Linf metric is a planar…
Planar Visibility: Testing and Counting
Joachim Gudmundsson, Pat Morin
In this paper we consider query versions of visibility testing and visibility counting. Let be a set of disjoint line segments in and let be an element of . V…