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.

Among these, shortest path queries are instrumental in identifying the most efficient routes within a network, thereby reducing cost, time and resource consumption.

We consider the shortest paths between all pairs of nodes in a directed or undirected complete graph with edge lengths which are uniformly and independently distributed in [0, 1].

There is a new sorting algorithm a deterministic O (m log2/3 n)-time algorithm for single-source shortest paths (SSSP) on directed graphs with real non-negative edge weights in the comparison-addition ...