graph-algorithm

问题 I am trying to write a divide & conquer algorithm for trees. For the divide step I need an algorithm that partitions a given undirected Graph G=(V,E) with n nodes and m edges into sub-trees by removing a node . All subgraphs should have the property that they don't contain more than n/2 nodes (the tree should be split as equal as possible). First I tried to recursively remove all leaves from the tree to find the last remaining node, then I tried to find the longest path in G and remove the

问题 I was wondering what is the time complexity of BFS, if I use: an adjacency matrix adjacency list edge list Is it same as their space complexity? 回答1: The complexity of BFS implemented using an Adjacency Matrix will be O(|V| 2 ). And that when implemented by an Adjacency List is O(|V| + |E|) . Why is it more in the case of Adjacency Matrix? This is mainly because every time we want to find what are the edges adjacent to a given vertex 'U', we would have to traverse the whole array

问题 Can someone explain the steps of the VF2 algorithm for graph isomorphism in simple words? I am learning this algorithm, but it is harsh without a working example. Can someone lead me the right direction? Thank you. 回答1: I will try to give you a quick explaination of my previous answer to this question : Any working example of VF2 algorithm? I will use the same example as the one in my previous answer : The 2 graphs above are V and V' .(V' is not in the drawing but it's the one on the right)

问题 The site http://web.eecs.utk.edu/~huangj/CS302S04/notes/graph-searching.html describes that when an adjacency list is used then, DFS and BFS have complexity O(V+E), and if an adjacency matrix is used, the complexity is O(V 2 ). Why is this? 回答1: In both cases, the runtime depends on how long it takes to iterate across the outgoing edges of a given node. With an adjacency list, the runtime is directly proportional to the number of outgoing edges. Since each node is visited once, the cost is

问题 I would like to find path of fixed length (given while running the program) in undirected graph. I'm using adjacency matrix of my graph. I tried to use some algorithms like DFS or A*, but they only return the shortest path. Nodes can't be visited again. So let's say that my graph have 9 nodes and the shortest path is built from 4 nodes. I want to have additional variable that will "tell" the algorithm that I want to find path which have 7 nodes (for example) and it will return nodes which are

问题 I would like to find path of fixed length (given while running the program) in undirected graph. I'm using adjacency matrix of my graph. I tried to use some algorithms like DFS or A*, but they only return the shortest path. Nodes can't be visited again. So let's say that my graph have 9 nodes and the shortest path is built from 4 nodes. I want to have additional variable that will "tell" the algorithm that I want to find path which have 7 nodes (for example) and it will return nodes which are

问题 I have to make an uninformed search (Breadth-first-Search) program which takes two nodes and return all the paths between them. public void BFS(Nod start, Nod end) { Queue<Nod> queue = new Queue<Nod>(); queue.Enqueue(start); while (queue.Count != 0) { Nod u = queue.Dequeue(); if (u == end) break; else { u.data = "Visited"; foreach (Edge edge in u.getChildren()) { if (edge.getEnd().data == "") { edge.getEnd().data = "Visited"; if (edge.getEnd() != end) { edge.getEnd().setParent(u); } else {

问题 I have a directed weighted graph G=(V,E), which may have loops . I am trying to determine the best time efficient algorithm to accomplish task: t o find all simple path in G between source and target node with total weight of edges in this path less than certain value (for convenience we denote this value as PATH_WEIGHT_LIMIT) All weights is positive and can be float. So, a prototype of my function will be: def find_paths(G, source, target, path_weight_limit) Result paths may overlap, its

问题 Please take a moment to understand my situation. If it is not comprehendable, please tell me in a comment. I have an ArrayList of Waypoints. These waypoints are not in any order. A waypoint has the following properties: {int type, float z, float y, float x, float rotation} This applies to a 3 dimensional world, but since my pathfinding should not care about height (and thus treat the world as a 2 dimensional one), the y value is ignored. Rotation is not of importance for this question. In

问题 I am working on a problem which could be reduced to a graph optimization problem as below. A set of colored nodes is given. They are all unconnected i.e. there is no edge in the graph. The edges are to be inserted between the nodes. A node can have only 4 edges at max. A table provides rules for profit contribution from the edges. Eg., An edge connecting red to red: profit is 10 An edge connecting red to blue: profit is 20 The total number of nodes is around 100. The total number of colors is