The stretch factor of a Euclidean graph is the maximum ratio of the distance in the graph between any two points and their Euclidean distance. Given a set S of n points in Rd, we ...
We present an improved oracle for the distance sensitivity problem. The goal is to preprocess a directed graph G = (V, E) with non-negative edge weights to answer queries of the f...
Let S be a set of n points in IRd and let t > 1 be a real number. A t-spanner for S is a graph having the points of S as its vertices such that for any pair p, q of points ther...
We prove a version of the derandomized Direct Product lemma for deterministic space-bounded algorithms. Suppose a Boolean function g : {0, 1}n {0, 1} cannot be computed on more th...
We explore the average-case “Vickrey” cost of structures in a random setting: the Vickrey cost of a shortest path in a complete graph or digraph with random edge weights; the V...