Shortest path algorithms

Average-case complexity of single-source shortest-paths algorithms: lower and upper bounds

“…Hence, at first glance, label-setting algorithms seem to be the better choice. However, several independent case studies [6,10,13,28,29,44,50,70] showed that SSSP implementations of label-correcting approaches frequently outperform labelsetting algorithms. Thus, worst-case analysis sometimes fails to bring out the advantages of algorithms that perform well in practice.…”

“…However, none of the alternative label-correcting algorithms succeeded to asymptotically improve on the O(n · m)-time worst-case bound of the simple BellmanFord approach. Still, a number of experimental studies [6,10,13,28,29,44,50,70] showed that some recent label-correcting approaches run considerably faster than the original Bellman-Ford algorithm and even outperform label-setting algorithms on certain data sets. So far, no profound average-case analysis has been given to explain the observed effects.…”

The combination of TOPSIS method and Dijkstra’s algorithm in multi-attribute routing

“…Dijkstra's algorithm is also known as the single-source shortest path algorithm which is similar to Prime's algorithm [29]. Using the Dijkstra's algorithm to nd the shortest path in the directed graph with a non-negative length is one of the basic and important issues in algorithmic problems [30,31]. Eklund [32] presented the modi ed Dijkstra's algorithm that includes both static and dynamic components, simultaneously used for routing the emergency vehicles in the simulation of earthquake in Okayama, Japan.…”

Bi-directional Search in QoS Routing

“…Ever since, many variations of shortest path algorithms have been proposed in the literature [8], [2], mainly based on different proposals for a priority queue [3]. Nearly all proposed shortest path algorithms are designed to Þnd a shortest paths tree rooted at the source to all other nodes.…”