Suppose we are given a sequence of n points in the Euclidean plane, and our objective is to construct, on-line, a connected graph that connects all of them, trying to minimize the...
Let (S, d) be a finite metric space, where each element p ∈ S has a non-negative weight w(p). We study spanners for the set S with respect to weighted distance function dw, wher...
Mohammad Ali Abam, Mark de Berg, Mohammad Farshi, ...
We introduce a new realistic input model for geometric graphs and nonconvex polyhedra. A geometric graph G is local if (1) the longest edge at every vertex v is only a constant fa...
Revisiting the “small-world” experiments of the ’60s, Kleinberg observed that individuals are very effective at constructing short chains of acquaintances between any two p...
The augmented graph model, as introduced by Kleinberg (STOC 2000), is an appealing model for analyzing navigability in social networks. Informally, this model is defined by a pair...