We establish upper and lower bounds on the number of connected components of lines tangent to four triangles in R3 . We show that four triangles in R3 may admit at least 88 tangent...
Given a set of n points in the plane, we show how to compute various enclosing isosceles triangles where different parameters such as area or perimeter are optimized. We then stud...
In the minimum-cost k-hop spanning tree (k-hop MST) problem, we are given a set S of n points in a metric space, a positive small integer k and a root point r ∈ S. We are intere...
Let S be a set system of convex sets in Rd . Helly’s theorem states that if all sets in S have empty intersection, then there is a subset S′ ⊂ S of size d+1 which also has e...