2 papers
cs.DS2025
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…
cs.DS2025
Negative-Weight Single-Source Shortest Paths in Near-linear Time
Aaron Bernstein, Danupon Nanongkai, Christian Wulff-Nilsen
We present a randomized algorithm that computes single-source shortest paths (SSSP) in time when edge weights are integral and can be negative. This essential…