What is the fastest Dijkstra implementation you know (in C++)?

Question

I did recently attach the 3rd version of Dijkstra algorithm for shortest path of single source into my project.

I realize that there are many different implementati

Answer 1

Two points I'd like to make: 1) Dijkstra vs A* Dijkstra's algorithm is a dynamic programming algorithm, not an heuristic. A* is an heuristic because it also uses an heuristic function (lets say h(x) ) to "estimate" how close a point x is getting to the end point. This information is exploited in subsequent decisions of which nodes to explore next.

For cases such as an Euclidean graph, then A* works well because the heuristic function is easy to define (one can simply use the Euclidean distance, for example). However, for non Euclidean graphs it may be harder to define the heuristic function, and a wrong definition can lead to a non-optimal path.

Therefore, dijkstra has the advantage over A* which is that it works for any general graph (with the exception of A* being faster in some cases). It could well be that certain implementations use these algorithms interchangeably, resulting in different results.

2) The dijkstra algorithm (and others such as A*) use a priority queue to obtain the next node to explore. A good implementation may use a heap instead of a queue, and an even better one may use a fibonacci heap. This could explain the different run times.

Answer 2

It's going to depend on a lot of things. How much do you know about your input data? Is it dense, or sparse? That will change which versions of the algorithm are the fastest.

If it's dense, just use a matrix. If its sparse, you might want to look at more efficient data structures for finding the next closest vertex. If you have more information about your data set than just the graph connectivity, then see if a different algorithm would work better like A*.

Problem is, there isn't "one fastest" version of the algorithm.

Answer 3

The best implementations known for road networks (>1 million nodes) have query times expressed in microseconds. See for more details the 9th DIMACS Implementation Challenge(2006). Note that these are not simply Dijkstra, of course, as the whole point was to get results faster.

Answer 4

May be I am not answering your question. My point is why to use Dijkstra when there are pretty much more efficient algorithms for your problem. If your graph fullfills the triangular property (it is an euclidian graph)

|ab| +|bc| > |ac|

(the distance from node a to node b plus distance from node b to node c is bigger than the distance from node a to node c) then you can apply the A* algorithm. This algorithm is pretty efficient. Otherwise consider using heuristics. The implementation is not the major issue. The algorithm to be used does matter.

Answer 5

The last time I checked, Dijkstra's Algorithm returns an optimal solution. All "true" implementations of Dijkstra's should return the same result each time.

Similarly, asymptotic analysis shows us that minor optimisations to particular implementations are not going to affect performance significantly as the input size increases.