minimum-spanning-tree

I am studying Prim's Algorithm. There is a part within the code the next vertex across the cut will be coming to the set of the vertices belonging to the MST . While doing that, we also have to 'update all vertices in the other set which are adjacent to the departing vertex'. This is a snapshot from CLRS : The interesting part lies in line no. 11. But since we are using a heap here, we have access to only the minimum element, right ( heap[0] )? So how do we search and update vertices from the heap even though they are not the minimum one and thus we have knowing where they are except by linear

I have an undirected connected graph G. I wish to find an algorithm that return true if there are at least 2 MSTs. What if I want to see if there are exactly 2 MSTs? j_random_hacker We can detect both cases efficiently by modifying the Kruskal algorithm. If someone can think of a simpler way to describe all this, please let me know! Kruskal builds an MST for every permutation of equal-weight edges The Kruskal algorithm builds an MST by always including the next-smallest edge that connects different components of the forest that has been built so far. The algorithm is correct whenever any such

A minimum bottleneck spanning tree of a weighted graph G is a spanning tree of G such that minimizes the maximum weight of any edge in the spanning tree. A MBST is not necessarily a MST (minimum spanning tree). Please give an example where these statements make sense. dan3 Look at the MST example on Wikipedia for reference: A bottleneck in a spanning tree is a maximum-weight edge in that tree. There may be several bottlenecks (all of the same weight of course) in a spanning tree. In the Wikipedia MST there are two bottlenecks of weight 8. Now, take a minimum spanning tree of a given graph

I have a symmetrical graph and created a tree with all shortest path from a random vertex to any other vertex. Can I use the tree to construct a Minimum Spanning Tree(MST)? My algorithm is similar to depth-first algorithm. In the worst case, a shortest path tree does not help in finding a minimum spanning tree. Consider a graph where we want to find the MST. Add a source vertex with edges of an identical large length to each other vertex. The shortest path tree from that source consists of the very long edges, which we knew a priori, hence the shortest path tree is not useful in this case. 来源：

Dijkstra's is typically used to find the shortest distance between two nodes in a graph. Can it be used to find a minimum spanning tree ? If so, how? Edit: This isn't homework, but I am trying to understand a question on an old practice exam. Strictly, the answer is no. Dijkstra's algorithm finds the shortest path between 2 vertices on a graph. However, a very small change to the algorithm produces another algorithm which does efficiently produce an MST. The Algorithm Design Manual is the best book I've found to answer questions like this one. Brian Cristante The answer is no. To see why, let

Possible Duplicate: All minimum spanning trees implementation How can I find all minimum spanning trees in an undirected graph in an efficient way? Apologies for the academic answer... but algorithm S in Knuth's TAOCP , Volume 4, Fascicle 4 is exactly about generating all spanning trees (pp. 26ff). There are a few musings when he talks about generating (spanning) trees, but your best bet in TAOCP. you can find one..modifying the BFS algorithm! Yes, there are algorithms for generating all spanning trees in a graph. At least one compresses the output by generating only diffs between the trees.

Suppose that you have a directed graph with nonnegative, integer edge lengths that are in the range 0 to U - 1, inclusive. What is the fastest algorithm for computing a minimum spanning tree of this graph? We can still use existing minimum spanning tree algorithms, such as Kruskal's algorithm O(m log n)) or Prim's algorithm (O(m + n log n)). However, for cases where U is small, I think it should be possible to do much better this. Are there any algorithms that are competitive with more traditional MST algorithms that are able to exploit the fact that the edge lengths are constrained to be in

I've been looking for an implementation (I'm using networkx library.) that will find all the minimum spanning trees (MST) of an undirected weighted graph. I can only find implementations for Kruskal's Algorithm and Prim's Algorithm both of which will only return a single MST. I've seen papers that address this problem (such as Representing all minimum spanning trees with applications to counting and generation ) but my head tends to explode someway through trying to think how to translate it to code. In fact i've not been able to find an implementation in any language! I don't know if this is