graph-theory

问题 I'm stuck at the following problem: Given a weighted digraph G, I'd like to construct the minimal subgraph of G that contains all negative (simple) cycles of G. I do know how to find a negative cycle using Bellman-Ford, and I know that the number of simple cycles in a directed graph is exponential. One naive way to approach the problem would be to simply iterate all simple cycles and pick those that are negative, but I have the feeling that there might be a polynomial-time algorithm. Most

问题 I have a DAG. I have this operation to add a edge between two nodes. If A is reachable from B, then B is A's parent. If A is reachable from B without going though another node, then B is A's direct parent. Requirements for this graph are: No cycles. For any node, there is a list of direct parents P[1],P[2],P[3]... P[i] is not a parent of P[j] for any i and j. If adding a edge, requirement 1 is not met, the edge is not constructed. If adding a edge, requirement 2 is not met, the edge is

问题 I'm trying to determine the cycles in a directed graph using Tarjan's algorithm, presented in his research paper "Enumeration of the elementary circuits of a directed graph" from Septermber 1972. I'm using Python to code the algorithm, and an adjacency list to keep track of the relationships between nodes. So in "G" below, node 0 points to node 1, node 1 points to nodes 4,6,7... etc. G = [[1], [4, 6, 7], [4, 6, 7], [4, 6, 7], [2, 3], [2, 3], [5, 8], [5, 8], [], []] N = len(G) points = []

问题 I have a directed acyclic graph with positive edge-weights. It has a single source and a set of targets (vertices furthest from the source). I find the shortest paths from the source to each target. Some of these paths overlap. What I want is a shortest path tree which minimizes the total sum of weights over all edges. For example, consider two of the targets. Given all edge weights equal, if they share a single shortest path for most of their length, then that is preferable to two mostly non

问题 I am trying to implement a randomly generated maze using Prim's algorithm. I want my maze to look like this: however the mazes that I am generating from my program look like this: I'm currently stuck on correctly implementing the steps highlighted in bold: Start with a grid full of walls. Pick a cell, mark it as part of the maze. Add the walls of the cell to the wall list. While there are walls in the list: **1. Pick a random wall from the list. If the cell on the opposite side isn't in the

问题 Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it's on-topic for Stack Overflow. Closed 5 years ago . I'm going to start a scientific project about automata and graph theory, and I'm searching for a graph library that supports features like: directed/undirected graphs graph isomorphism test (i.e. is graph g1 isomorphic w.r.t. g2?) subgraph isomorphism test (i.e. is a graph g1 isomorphic to a subgraph of g2?)

问题 One of the assignments in my algorithms class is to design an exhaustive search algorithm to solve the clique problem. That is, given a graph of size n , the algorithm is supposed to determine if there is a complete sub-graph of size k . I think I've gotten the answer, but I can't help but think it could be improved. Here's what I have: Version 1 input : A graph represented by an array A[0,... n -1], the size k of the subgraph to find. output : True if a subgraph exists, False otherwise

问题 in words, can someone post directions towards finding the 'maximal' independent set in a simple graph? I read up something from ETH site which said one can find such in O(n) by simply picking a random vertex v and than scanning the rest and attempting to find if there's an edge from v to the rest. Thanks 回答1: Yes, by definition, a maximal indpendent set is an independent set to which no more vertices can be added without violating the 'independence' condition. So just picking vertices till

问题 If I have an undirected graph, how can I get a list of all cycles? For example, from the following graph, I would want the cycles: (a,b,d,e,c) (a,b,c) (b,d,e) 回答1: You presumably want only simple cycles (those that don't repeat a vertex), or there's an infinite number of them. Even then, there can be an exponential number of cycles. Perhaps this isn't the problem you really want to solve? 回答2: this is not possible in polynomial time as if possible then we could use this to find all cycles and

问题 I quote from Artificial Intelligence: A Modern Approach: The properties of depth-first search depend strongly on whether the graph-search or tree-search version is used. The graph-search version, which avoids repeated states and redundant paths, is complete in finite state spaces because it will eventually expand every node. The tree-search version, on the other hand, is not complete [...]. Depth-first tree search can be modified at no extra memory cost so that it checks new states against