Question

I am trying to profile the speed of A* and Dijkstra algorithm. I am using the code available at http://www.boost.org/doc/libs/1_38_0/libs/graph/example/astar-cities.cpp and http://www.boost.org/doc/libs/1_50_0/libs/graph/doc/dijkstra_shortest_paths.html. I tried a simple graph with 500 edges and 300 nodes.

I was expecting A* to perform better than Dijkstra since in Dijkstra the shortest distance from the source vertex to every other vertex is found. On the other hand in A* the shortest distance to the goal node is only found.

However, profiling showed that Dijkstra performed slightly better than A*. Is it possible or I am missing something?

Answer 1

Djikstra’s algorithm uses a queue while A* uses a priority queue. In general, queues will perform better than priority queues (eg. enqueue/dequeue from a queue using a linked-list or circular-array is O(1), while enqueue/dequeue from a priority queue using a heap is O(log n)).

However, again in general, the cases where this small difference causes A* to run slower than Djikstra’s tend to be the cases where both algorithms run extremely fast anyways – in small mazes, and mazes with only a small number of paths to consider (such as a zig-zagging maze). In the slower cases (out in the open with few obstacles), A
* should run much faster.

Since your case has 300-nodes, there’s a good chance there’s something wrong with your code. Without seeing it, we can’t help you any further.