minimum-spanning-tree

问题 I am doing my project on graph matching in hand written image, i want to represent a given word image in graph, am using the below algorithm Algorithm: input: Binary image B, Grid width w, Grid height h Output: Graph g = (V, E) with nodes V and edges E 1: function Grid(B,w,h) 2: for i ← 1 to number of columns C = Width of B/w do 3: for j ← 1 to number of rows R = Height of B/h do 4: V = V ∪ {(xm, ym) | (xm, ym) is the centre of mass of segment sij} 5: for Each pair of nodes (u, v) ∈ V × V do

问题 I am doing my project on graph matching in hand written image, i want to represent a given word image in graph, am using the below algorithm Algorithm: input: Binary image B, Grid width w, Grid height h Output: Graph g = (V, E) with nodes V and edges E 1: function Grid(B,w,h) 2: for i ← 1 to number of columns C = Width of B/w do 3: for j ← 1 to number of rows R = Height of B/h do 4: V = V ∪ {(xm, ym) | (xm, ym) is the centre of mass of segment sij} 5: for Each pair of nodes (u, v) ∈ V × V do

问题 A graph can have many different Minimum Spanning Trees (MSTs), but can different MSTs have different sets of edge weights? For example, if an MST uses edge weights {2,3,4,5}, must every other MST have edge weights {2,3,4,5}, or can some other MST use a different collection of weights? What gave me the idea is property that a graph has no unique MST only if its edge weights are different. 回答1: The sets must have the same weight. Here's a simple proof: suppose they don't. Let's let T1 and T2 be

问题 A graph (positive weight edges) with a MST If some edge, e is modified to a new value, what is the best way to update the MST without completely remaking it. I think this can be done in linear time. Also, it seems that I would need a different algorithm based on whether 1) e is already a part of the MST and 2) whether the new edge, e is larger or smaller than the original 回答1: There are 4 cases: Edge is in MST and you decreasing value of edge: Current MST is still MST Edge is not in MST and

问题 Prim’s Algorithm An algorithm for finding a minimum spanning tree. Begin by choosing any edge with smallest weight, putting it into the spanning tree. Successively add to the tree edges of minimum weight that are incident to a vertex already in the tree, never forming a simple circuit with those edges already in the tree. Stop when n − 1 edges have been added. I know that you must start at node A. Also by giving a list of the order in which nodes and/or edges are added. But im not sure on the

问题 Hi awesome person! I have a problem... I get a NullPointerException when my test case reaches allEdges.add(newEdge); in the connectNodes method. I think it has something to do with Edge newEdge = new Edge( n1, n2, weight ); previously in that same method. Is the problem my use of generics in the Edge class or something like that?. I previously got an error directing me at the Edge newEdge = new Edge( n1, n2, weight ); line, saying something like "class not found". But now i seem to get the

问题 I asked this question on reddit, but haven't converged on a solution yet. Since many of my searches bring me to Stack Overflow, I decided I would give this a try. Here is a simple formulation of my problem: Given a weighted undirected graph G(V,E,w) and a subset of vertices S in G, find the min/max weight tree that spans S. Adding vertices is not allowed. An extension of the basic model is adding edges with 0 weight, and vertices that must be excluded. This seems similar to the question asked

问题 I am trying to modify the minimum spanning tree if the weight of an edge in the graph not belonging to MST is decreased.I read on stackoverflow that first connect the edge to the MST now there is exactly one cycle in MST and by cycle property the edge whose weight is maximum in cycle can be deleted from MST? How to find the max weight edge in that cycle? 回答1: Let the new edge added be between node i and j .There will be exactly one cycle containing all nodes between node i and j , including

问题 I am trying to modify the minimum spanning tree if the weight of an edge in the graph not belonging to MST is decreased.I read on stackoverflow that first connect the edge to the MST now there is exactly one cycle in MST and by cycle property the edge whose weight is maximum in cycle can be deleted from MST? How to find the max weight edge in that cycle? 回答1: Let the new edge added be between node i and j .There will be exactly one cycle containing all nodes between node i and j , including

问题 Given a weighted, connected, simple undirected graph G with weights of only 1 and 2 on each edge, find the MST of G in O(V+E). Any ideas? Sorry for the phrasing of the question, I tried translating it as best as I could. 回答1: In Prim's algorithm you need a way of storing active edges such that you can access and delete the edge with lowest weight. Normally there are a wide range of weights and some kind of heap data structure is used to store the edges. However, in this case, the weights are