How to optimize Dijkstra algorithm for a single shortest path between 2 nodes?

Question

I was trying to understand this implementation in C of the Dijkstra algorithm and at the same time modify it so that only the shortest path between 2 specific nodes (source

Answer 1

You could perhaps improve somewhat by maintaining a separate open and closed list (visited and unvisited) it may improve seek times a little.

Currently you search for an unvisited node with the smallest distance to source.

1) You could maintain a separate 'open' list that will get smaller and smaller as you iterate and thus making your search space progressively smaller.

2) If you maintain a 'closed' list (those nodes you visited) you can check the distance against only those nodes. This will progressively increasing your search space but you don't have to check all nodes each iteration. The distance check against nodes that have not been visited yet holds no purpose.

Also: perhaps consider following the graph when picking the next node to evaluate: On the 'closed' list you could seek the smallest distance and then search an 'open' node among it's connections. (if the node turns out to have no open nodes in it's connections you can remove it from the closed list; dead end). You can even use this connectivity to form your open list, this would help with islands also (your code will currently crash if you graph has islands).

You could also pre-build a more efficient connection graph instead of a cross table containing all possible node combinations (eg. a Node struct with a neighbours[] node list). This would remove having to check all nodes for each node in the dist[][] array

Instead of initializing all node distances to infinity you could initialize them to the 'smallest possible optimistic distance' to the target and favor node processing based on that (your possibilities differ here, if the nodes are on a 2D plane you could use bird-distance). See A* descriptions for the heuristic. I once implemented this around a queue, not entirely sure how I would integrate it in this code (without a queue that is).