In a weighted graph or network, travelling becomes more complex as optimising resources, such as time or cost, must be considered. This is where finding the shortest path plays a critical role in ...

By making progress on one of the most intriguing and well-studied graph theoretic problems, the paper proposes a new way of designing efficient graph algorithms that will go significantly beyond ...

Bellman-Ford algorithm So what do we do when we have negative weights? As long as there are no negative cycles in our weighted directed graph we can use the Bellman-Ford algorithm. Like Dijkstra’s ...

Shortest path mining is one of the classic problems in graph theory. How to design an efficient multi-source shortest paths mining algorithm has practical significance. In this article, an efficient ...

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.