Abstract: The shortest path problem is to find a path between two vertices (nodes) on a given graph, such that the sum of the weights on its constituent edges is minimized. This problem has been ...

A recent breakthrough of Bernstein, Nanongkai, and Wulff-Nilsen established the first near-linear time algorithm for negative-weight single-source shortest paths on integer-weighted graphs. We refine ...

Modern technology runs on algorithms, but one stands above all others in terms of impact. From computing and communication to science and everyday digital life, this algorithm quietly shaped how the ...

Shortest path algorithms sit at the heart of modern graph theory and many of the systems that move people, data, and goods around the world. After nearly seventy years of relying on the same classic ...

A header-only C++ implementation of the single-source shortest path (SSSP) algorithm for sparse directed graphs with non-negative weights, based on the 2025 paper by Duan et al. This algorithm is ...

For the low efficiency and poor generalization ability of path planning algorithm of industrial robots, this work proposes an adaptive field co-sampling algorithm (AFCS). Firstly, the environment ...

When Edsger W. Dijkstra published his algorithm in 1959, computer networks were barely a thing. The algorithm in question found the shortest path between any two nodes on a graph, with a variant ...

The original version of this story appeared in Quanta Magazine. If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle ...