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...
Abstract. In a seminal STOC'95 paper, Arya et al. [4] devised a construction that for any set S of n points in Rd and any > 0, provides a (1 + )-spanner with diameter O(lo...
We show that for every set S of n points in the plane and a designated point rt ∈ S, there exists a tree T that has small maximum degree, depth and weight. Moreover, for every po...
Integration over a domain, such as a Euclidean space or a Riemannian manifold, is a fundamental problem across scientific fields. Many times, the underlying domain is only acces...
Θk-graphs are geometric graphs that appear in the context of graph navigation. The shortest-path metric of these graphs is known to approximate the Euclidean complete graph up to...
Nicolas Bonichon, Cyril Gavoille, Nicolas Hanusse,...