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Looking for K-Shortest Path High Level Pseudocode

post #1 of 7
Thread Starter 
I'm trying to find a high level description of a k-shortest path algorithm such as Yen's.

For example, this is a high level description of Suurballe's algorithm:

Quote:
Find the shortest path tree T rooted at node s by running Dijkstra's algorithm. This tree contains for every vertex u, a shortest path from s to u. Let P1 be the shortest cost path from s to t. The edges in T are called tree edges and the remaining edges are called non tree edges.

Modify the cost of each edge in the graph by replacing the cost w(u,v) of every edge (u,v) by w'(u,v) = w(u,v) − d(s,v) + d(s,u). According to the resulting modified cost function, all tree edges have a cost of 0, and non tree edges have a non negative cost.

Create a residual graph Gt formed from G by removing the edges of G that are directed into s and by reversing the direction of the zero length edges along path P1.

Find the shortest path P2 in the residual graph Gt by running Dijkstra's algorithm.

Discard the reversed edges of P2 from both paths. The remaining edges of P1 and P2 form a subgraph with two outgoing edges at s, two incoming edges at t, and one incoming and one outgoing edge at each remaining vertex. Therefore, this subgraph consists of two edge-disjoint paths from s to t and possibly some additional (zero-length) cycles. Return the two disjoint paths from the subgraph
A lot of the pseudocode I've been able to find for k-shortest assumes particular ways of defining graphs, paths, nodes, edges, etc and therefore they aren't very useful for what I need.
post #2 of 7
Bump, simply because I want to know what the hell is the OP is about
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post #3 of 7
i couldnt find much on yen's algorithm but i believe the Floyd–Warshall algorithm is also a k shortest path algorithm. wikipedia has some good pseudo code for it. https://secure.wikimedia.org/wikiped...thm#Pseudocode

i hope this is what you're looking for. good luck with whatever you need this for
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post #4 of 7
I don't know about pseudocode, but I wrote this a couple of years ago:

Fair warning, this isn't pseudocode, it is complete code, C++.

http://pastebin.com/uQ2HNCAq
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post #5 of 7
Thread Starter 
Quote:
Originally Posted by travesty View Post
i couldnt find much on yen's algorithm but i believe the Floyd–Warshall algorithm is also a k shortest path algorithm. wikipedia has some good pseudo code for it. https://secure.wikimedia.org/wikiped...thm#Pseudocode

i hope this is what you're looking for. good luck with whatever you need this for
The Floyd-Warshall is just an all-pair shortest path algorithm.

Quote:
Originally Posted by lordikon View Post
I don't know about pseudocode, but I wrote this a couple of years ago:

Fair warning, this isn't pseudocode, it is complete code, C++.

http://pastebin.com/uQ2HNCAq
Dijkstra's is also just a shortest path algorithm.

I'm looking for an algorithm that will find the k-shortest paths between a given source/destination pair.

So if k = 3, it would return the shortest path, the second shortest path, and the third shortest path.
post #6 of 7
Quote:
Originally Posted by TEntel View Post
The Floyd-Warshall is just an all-pair shortest path algorithm.



Dijkstra's is also just a shortest path algorithm.

I'm looking for an algorithm that will find the k-shortest paths between a given source/destination pair.

So if k = 3, it would return the shortest path, the second shortest path, and the third shortest path.
I see, I misunderstood the question. You might be able to modify the Dijkstra's to follow all paths rather than ignore longer paths, store the results, and return the top k results to you.
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post #7 of 7
Thread Starter 
Yeah, all k-path algorithms I've seen start by using Dijkstra's to find a shortest path tree from one node, to all other nodes. I already have code in place that does that.

There are plenty of journal / conference papers that deal with k-shortest path algorithms, but without understanding the general principle of k-shortest path, it is difficult to read the low-level mathematical explanations.
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