We present a randomized algorithm that computes single-source shortest paths (SSSP) in
O\left(m\log^8(n)\logW\right) time when edge weights are integral and can be negative. 1 …

Exact computation of shortest paths in weighted graphs has been traditionally studied in one
of two settings. First, one can assume that the edge weights are real numbers and all the …

This paper presents parallel, distributed, and quantum algorithms for single-source shortest
paths when edges can have negative integer weights (negative-weight SSSP). We show a …

We give the first parallel algorithm with optimal $\tilde {O}(m) $ work for the classical problem
of computing Single-Source Shortest Paths in general graphs with negative-weight edges. In …

Historic Algorithms Help Unlock Shortest-Path Problem Breakthrough Page 1 In finance, for
example, there may be situations in currency or options trading where buying and selling in …

The textbook algorithm for single-source shortest paths with real-valued edge weights runs
in $ O (mn) $ time on a graph with $ m $ edges and $ n $ vertices. A recent breakthrough …

This paper is about the problem of finding a shortest $ s $-$ t $ path using at most $ h $
edges in edge-weighted graphs. The Bellman--Ford algorithm solves this problem in $ O …

This paper presents a randomized algorithm for single-source shortest paths on directed
graphs with real (both positive and negative) edge weights. Given an input graph with n …

We study the maximum s, t-flow oracle problem on planar directed graphs where the goal is
to design a data structure answering max s, t-flow value (or equivalently, min s, t-cut value) …

Vizing's celebrated theorem states that every simple graph with maximum degree $\Delta $
admits a $(\Delta+ 1) $ edge coloring which can be found in $ O (m\cdot n) $ time on $ n …