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 ...

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.

So all shortest paths must be of length at most k. <BR><BR>One solution, which works well for small k, is to run the Bellman-Ford algorithm (slightly modified) for k steps. This takes O (km) time.

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

Unfortunately, prior research does not provide a clear direction for choosing an algorithm when one faces the problem of computing shortest paths on real road networks. Most of the computational ...