5 papers
Shortcutting for Negative-Weight Shortest Path
George Z. Li, Jason Li, Satish Rao +1
Consider the single-source shortest paths problem on a directed graph with real-valued edge weights. We solve this problem in time, improving on prior work…
Faster Weak Expander Decompositions and Approximate Max Flow
Henry Fleischmann, George Z. Li, Jason Li
We give faster algorithms for weak expander decompositions and approximate max flow on undirected graphs. First, we show that it is possible to "warm start" the cut-matching game w…
Reviving Thorup's Shortcut Conjecture
Aaron Bernstein, Henry Fleischmann, Maximilian Probst Gutenberg +7
We aim to revive Thorup's conjecture [Thorup, WG'92] on the existence of reachability shortcuts with ideal size-diameter tradeoffs. Thorup originally asked whether, given any graph…
Fast Algorithms for Graph Arboricity and Related Problems
Ruoxu Cen, Henry Fleischmann, George Z. Li +2
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m…
Improved Directed Expander Decompositions
Henry Fleischmann, George Z. Li, Jason Li
We obtain faster expander decomposition algorithms for directed graphs, matching the guarantees of Saranurak and Wang (SODA 2019) for expander decomposition on undirected graphs. O…