Modify Dijkstra algorithm to find the shortest path

Asked May 11 '16 at 16:45

Active May 11 '16 at 16:51

Viewed 453 times

Here is Dijkstra pseudocode:

Dijkstra(G,s) {
foreach vεV do { d[v] = infinity }
Queue priority initialization Q with n elements
Q = V
d[s] = 0
while(Q is not empty) {
    v = ExtractMin(Q)
    foreach e = (v,w) ε E do
        if d(w) > d(v) + l {
            d(w) = d(v) + l //reduce priority
            ChangeKey(Q,w,d[w]) //reduce key
        }
    }
}

How can i modify this algorithm to find the shortest path that also has the smallest number of edges among all shortest paths.

edited May 11 '16 at 16:51

amit

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asked May 11 '16 at 16:45

Lee Yaan

1

I haven't looked closely at your pseudocode, but Dijkstra's algorithm does exactly that already. What are you trying to do that Dijkstra's isn't doing for you already? – Erick G. Hagstrom May 11 '16 at 16:48
@ErickG.Hagstrom I think he's after finding the path, and not just its length. – amit May 11 '16 at 16:48
i want to find the smallest paths with smallest number of edges – Lee Yaan May 11 '16 at 16:50
1

Set all of your edge lengths to 1. – Erick G. Hagstrom May 11 '16 at 16:51
1

If amongst all shortest paths, you want to find one with minimal number of edges, you can use vectors (w, 1) as edge weights and use lexicographical comparisons – Niklas B. May 11 '16 at 16:53
@Nicklas B. can you explain me which points have i to change in my pseudocode? – Lee Yaan May 11 '16 at 17:06
2

Just replace `l` by `(l, 1)`. Although you did not define `l`, I assume it is the length of the edge `(v, w)` – Niklas B. May 11 '16 at 17:16
yes l is the length of the edge. So i changed only the l with 1 – Lee Yaan May 11 '16 at 17:43
That was not was I suggested though. I meant replacing `l` by the vector `(l, 1)` and using component-wise addition and lexicographic comparison – Niklas B. May 15 '16 at 13:18

Modify Dijkstra algorithm to find the shortest path

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