Euclidean spanners are important geometric structures, having found numerous
applications over the years. Cornerstone results in this area from the late 1980s and early …

This paper presents the first distributed algorithm to construct a spanner for arbitrary ad hoc
networks under the physical signal-to-interference-and-noise-ratio (SINR) interference …

Spanners for metric spaces have been extensively studied, perhaps most notably in low-
dimensional Euclidean spaces-due to their numerous applications. Euclidean spanners can …

The notion of distance is fundamental to many aspects of computational geometry. A classic
approach to characterize the distance properties of planar (and high-dimensional) point sets …

Given a set of points in the plane, we show that the θ-graph with 5 cones is a geometric
spanner with spanning ratio at most 50+ 22 5≈ 9.960. This is the first constant upper bound …

We present a deterministic local routing algorithm that is guaranteed to find a path between
any pair of vertices in a half-\theta_6-graph (the half-\theta_6-graph is equivalent to the …

A well-known clustering problem called Density-Based Spatial Clustering of Applications
with Noise~(DBSCAN) involves computing the solutions of at least one disk range query per …

Spanner construction is one of the most important techniques for topology control in wireless
networks. A spanner can help not only to decrease the number of links and to maintain …

Yao graphs are geometric spanners that connect each point of a given point set to its
nearest neighbor in each of $ k $ cones drawn around it. Yao graphs were introduced to …

The classic method to depict graphs is a node-link diagram where vertices (nodes) are
associated with each object and edges (links) connect related objects. However, node-link …