tarjans-algorithm

Tarjan's strongly-connected components algorithm - why index in the back edge?

由 无人久伴 提交于 2021-02-04 18:08:11
问题 I'm studying Tarjan's algorithm for strongly-connected components and the way it works is clear to me. Anyway there's a line I don't understand: // Consider successors of v for each (v, w) in E do if (w.index is undefined) then // Successor w has not yet been visited; recurse on it strongconnect(w) v.lowlink := min(v.lowlink, w.lowlink) else if (w.onStack) then // Successor w is in stack S and hence in the current SCC v.lowlink := min(v.lowlink, w.index) // ************* end if end for I

Tarjan's strongly-connected components algorithm - why index in the back edge?

由 随声附和 提交于 2021-02-04 18:05:48
问题 I'm studying Tarjan's algorithm for strongly-connected components and the way it works is clear to me. Anyway there's a line I don't understand: // Consider successors of v for each (v, w) in E do if (w.index is undefined) then // Successor w has not yet been visited; recurse on it strongconnect(w) v.lowlink := min(v.lowlink, w.lowlink) else if (w.onStack) then // Successor w is in stack S and hence in the current SCC v.lowlink := min(v.lowlink, w.index) // ************* end if end for I

Enumerating cycles in a graph using Tarjan's algorithm

由 断了今生、忘了曾经 提交于 2020-01-01 05:37:08
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 = []

Non-recursive version of Tarjan's algorithm

由 ∥☆過路亽．° 提交于 2019-12-23 05:43:29
问题 I have the following (recursive) implementation of Tarjan's algorithm to find strongly connected components in a graph and it works fine: public class StronglyConnectedComponents { public static List<List<int>> Search(Graph graph) { StronglyConnectedComponents scc = new StronglyConnectedComponents(); return scc.Tarjan(graph); } private int preCount; private int[] low; private bool[] visited; private Graph graph; private List<List<int>> stronglyConnectedComponents = new List<List<int>>();

How do I learn Tarjan's algorithm?

由 大兔子大兔子 提交于 2019-12-21 03:34:22
问题 I have been trying to learn Tarjan's algorithm from Wikipedia for 3 hours now, but I just can't make head or tail of it. :( http://en.wikipedia.org/wiki/Tarjan's_strongly_connected_components_algorithm#cite_note-1 Why is it a subtree of the DFS tree? (actually DFS produces a forest? o_O) And why does v.lowlink=v.index imply that v is a root? Can someone please explain this to me / give the intuition or motivation behind this algorithm? 回答1: The idea is: When traversing the tree, every time

Tarjan's algorithm: do lowest-links have to be similar for two or more nodes to be inside the same SCC

由 三世轮回 提交于 2019-12-10 20:28:53
问题 I'm having some trouble with a homework question involving using Tarjan's algorithm on a provided graph to find the particular SCC's for that graph. While (according to my professor) I have found the correct SCC's by using the pseudo-code algorithm found here, some of the nodes in my SCC's do not share the same lowest-link number as the root node for that SCC. From what I can gather from the pseudo-code, this is because if an un-referenced node i (which is the input node for the current

Does Tarjan's SCC algorithm give a topological sort of the SCC?

由 时光怂恿深爱的人放手 提交于 2019-12-04 18:48:51
问题 I've been studying SCC and algorithms about them, and I've seen that people almost always mention that Kosaraju's algorithm finds the SCC and also gives them ordered in a (reversed) topological sort. My question is: doesn't Tarjan's algorithm also find a (reversed) topological sort? I've found that it isn't mentioned (at least from where I've read, except wikipedia). I've been thinking about it and make perfect sense. When tarjans_dfs is called on some node u, all SCCs that are reachable from

Tarjan's strongly connected components algorithm in python not working

由 断了今生、忘了曾经 提交于 2019-12-04 09:12:56
问题 I implemented the Tarjan's strongly connected components algorithm, according to wikipedia, in Python, but it isn't working. The algorithm is quite short and I cannot find any difference, so I cannot tell why it isn't working. I tried to check the original paper, but could not find it. Here is the code. def strongConnect(v): global E, idx, CCs, c, S idx[v] = (c, c) #idx[v][0] for v.index # idx[v][1] for v.lowlink c += 1 S.append(v) for w in [u for (v2, u) in E if v == v2]: if idx[w][0] < 0:

Tarjan's Algorithm: Time Complexity and slight modification possibility

由 有些话、适合烂在心里 提交于 2019-12-04 05:08:36
问题 This question is related to but not the same as the one recently asked here. I just read the Wikipedia psuedocode. algorithm tarjan is input: graph G = (V, E) output: set of strongly connected components (sets of vertices) index := 0 S := empty for each v in V do if (v.index is undefined) then strongconnect(v) end if end for function strongconnect(v) // Set the depth index for v to the smallest unused index v.index := index v.lowlink := index index := index + 1 S.push(v) // Consider

Enumerating cycles in a graph using Tarjan's algorithm

由 生来就可爱ヽ(ⅴ＜●) 提交于 2019-12-03 16:57:59
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 = [] marked_stack = [] marked = [False for x in xrange(0,N)] g = None def tarjan(s, v, f): global g points
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