In such cases, the fastest known shortest-path algorithm doesn’t work. For decades, fast algorithms for finding shortest paths on negative-weight graphs have remained elusive.

A canonical problem in computer science is to find the shortest route to every point in a network. A new approach beats the classic algorithm taught in textbooks.

Russell Eveleigh is using a Raspberry Pi Pico to demonstrate Dijkstra's algorithm visually with LEDs arranged as a map of the Cotswolds in England.

However, when the traditional Dijkstra algorithm solves the shortest path between nodes, a large number of nodes outside the identified nodes are calculated, which affects the speed of the algorithm.

Quantitative Improvement Old Bound (Dijkstra): O (m+nlog⁡n)O (m+nlogn) New Bound: O (mlog⁡2/3n)O (mlog2/3n) For sparse graphs where mm is about O (n)O (n), this is asymptotically faster as nn grows.