5 papers
DAG Covers: The Steiner Point Effect
Sujoy Bhore, Hsien-Chih Chang, Jonathan Conroy +4
Given a weighted digraph , a -DAG cover is a collection of dominating DAGs such that all distances are approximately preserved: for every pair $(u,…
Are there graphs whose shortest path structure requires large edge weights?
Aaron Bernstein, Greg Bodwin, Nicole Wein
The aspect ratio of a (positively) weighted graph is the ratio of its maximum edge weight to its minimum edge weight. Aspect ratio commonly arises as a complexity measure in gr…
Beyond 2-approximation for k-Center in Graphs
Ce Jin, Yael Kirkpatrick, Virginia Vassilevska Williams +1
We consider the classical -Center problem in undirected graphs. The problem is known to have a polynomial-time 2-approximation. There are even -approximations r…
Detecting Disjoint Shortest Paths in Linear Time and More
Shyan Akmal, Virginia Vassilevska Williams, Nicole Wein
In the -Disjoint Shortest Paths (-DSP) problem, we are given a weighted graph on nodes and edges with specified source vertices , and target vert…
Additive Spanner Lower Bounds with Optimal Inner Graph Structure
Greg Bodwin, Gary Hoppenworth, Virginia Vassilevska Williams +2
We construct -node graphs on which any -size spanner has additive error at least , improving on the previous best lower bound of [Bodwin-Hoppe…