Consider the Delaunay triangulation T of a set P of points in the plane as a Euclidean graph,
in which the weight of every edge is its length. It has long been conjectured that the stretch …

Consider the Delaunay triangulation T of a set P of points in the plane. The spanning ratio of
T, ie the maximum ratio between the length of the shortest path between this pair on the …

Given a graph embedded in a metric space, its dilation is the maximum over all distinct pairs
of vertices of the ratio between their distance in the graph and the metric distance between …

Let us consider the network of streets of a city represented by a geometric graph G in the
plane. The vertices of G represent the crossroads and the edges represent the streets. The …

Let G=(V, E) be an undirected graph with n vertices embedded in a metric space. We
consider the problem of adding a shortcut edge in G that minimizes the dilation of the …

We develop a property testing algorithm with query complexity ̃O(δ^-5dϵ^-5Dlog^6Δn) that
tests whether a directed geometric graph G=(P, E) with maximum degree D and vertex set …

Let C be a polygonal cycle on n vertices in the plane. A randomized algorithm is presented
which computes in O (n log 3 n) expected time, the edge of C whose removal results in a …

A feed-link is an artificial connection from a given location p to a real-world network. It is
most commonly added to an incomplete network to improve the results of network analysis …

Road network data is often incomplete, making it hard to perform network analysis. This
paper discusses the problem of extending partial road networks with reasonable links, using …

Given a geometric graph G with n vertices and m edges, we look at the problem of
augmenting G with an edge such that the dilation of the resulting graph is minimized. This …