We consider segment intersection searching amidst (possibly intersecting) algebraic arcs in the plane. We show how to preprocess n arcs in time O(n2+ ) into a data structure of si...
In a Batched Colored Intersection Searching Problem (CI), one is given a set of n geometric objects (of a certain class). Each object is colored by one of c colors, and the goal i...
Given a set S of segments in the plane, a polygon P is an intersecting polygon of S if every segment in S intersects the interior or the boundary of P. The problem MPIP of computi...
We show that recognizing intersection graphs of convex sets has the same complexity as deciding truth in the existential theory of the reals. Comparing this to similar results on t...
Consider a family of sets and a single set, called the query set. How can one quickly find a member of the family which has a maximal intersection with the query set? Time constra...
Benjamin Hoffmann, Mikhail Lifshits, Yury Lifshits...