Building on the work of Martinetz, Schulten and de Silva, Carlsson, we introduce a 2-parameter family of witness complexes and algorithms for constructing them. This family can be ...
Dominique Attali, Herbert Edelsbrunner, John Harer...
We introduce a family of directed geometric graphs, denoted Gθ λ, that depend on two parameters λ and θ. For 0 ≤ θ < π 2 and 1 2 < λ < 1, the Gθ λ graph is a s...
In this paper, we give a O(log copt)-approximation algorithm for the point guard problem where copt is the optimal number of guards. Our algorithm runs in time polynomial in n, the...
Ajay Deshpande, Taejung Kim, Erik D. Demaine, Sanj...
In this paper we explore, from an algorithmic point of view, the extent to which the facial angles and combinatorial structure of a convex polyhedron determine the polyhedron—in ...
We consider the problem of computing the centroid of all the vertices in a non-degenerate arrangement of n lines. The trivial approach requires the enumeration of all `n 2 ´ verti...
Deepak Ajwani, Saurabh Ray, Raimund Seidel, Hans R...