clique-problem | 易学教程

max-weight k-clique in a complete k-partite graph

阅读更多关于 max-weight k-clique in a complete k-partite graph

问题 My Problem Whether there's an efficient algorithm to find a max-weight (or min-weight) k -clique in a complete k -partite graph (a graph in which vertices are adjacent if and only if they belong to different partite sets according to wikipedia)? More Details about the Terms Max-weight Clique: Every edge in the graph has a weight. The weight of a clique is the sum of the weights of all edges in the clique. The goal is to find a clique with the maximum weight. Note that the size of the clique

Clique problem algorithm design

阅读更多关于 Clique problem algorithm design

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

Finding All Cliques of an Undirected Graph

阅读更多关于 Finding All Cliques of an Undirected Graph

问题 How can I list all cliques of an Undirected Graph ? (Not all maximal cliques, like the Bron-Kerbosch algorithm) 回答1: The optimal solution is like this because in a complete graph there are 2^n cliques. Consider all subsets of nodes using a recursive function. And for each subset if all the edges are present between nodes of the subset, add 1 to your counter: (This is almost a pseudocode in C++) int clique_counter = 0; int n; //number of nodes in graph //i imagine nodes are numbered from 1 to

Reduction to Clique prob

阅读更多关于 Reduction to Clique prob

问题 Subgraph isomorphism We have the graphs G_1=(V_1,E_1), G_2=(V_2,E_2). Question : Is the graph G_1 isomorphic to a subgraph of G_2 ? (i.e. is there a subset of vertices of G_2, V ⊆ V_2 and subset of the edges of G_2, E ⊆ E_2 such that |V|=|V_1| and |E|=|E_1| and is there a one-to-one matching of the vertices of G_1 at the subset of vertices V of G_2, f:V_1 -> V such that {u,v} ∈ E_1 <=> { f(u),f(v) } ∈ E) Show that the problem Subgraph isomorphism belongs to NP. Show that the problem is NP

Reduction to Clique prob

阅读更多关于 Reduction to Clique prob

Implementing Bron–Kerbosch algorithm in python

阅读更多关于 Implementing Bron–Kerbosch algorithm in python

问题 for a college project I'm trying to implement the Bron–Kerbosch algorithm, that is, listing all maximal cliques in a given graph. I'm trying to implement the first algorithm (without pivoting) , but my code doesn't yield all the answers after testing it on the Wikipedia's example , my code so far is : # dealing with a graph as list of lists graph = [[0,1,0,0,1,0],[1,0,1,0,1,0],[0,1,0,1,0,0],[0,0,1,0,1,1],[1,1,0,1,0,0],[0,0,0,1,0,0]] #function determines the neighbors of a given vertex def N

Implementing Bron–Kerbosch algorithm in python

阅读更多关于 Implementing Bron–Kerbosch algorithm in python

for a college project I'm trying to implement the Bron–Kerbosch algorithm , that is, listing all maximal cliques in a given graph. I'm trying to implement the first algorithm (without pivoting) , but my code doesn't yield all the answers after testing it on the Wikipedia's example , my code so far is : # dealing with a graph as list of lists graph = [[0,1,0,0,1,0],[1,0,1,0,1,0],[0,1,0,1,0,0],[0,0,1,0,1,1],[1,1,0,1,0,0],[0,0,0,1,0,0]] #function determines the neighbors of a given vertex def N(vertex): c = 0 l = [] for i in graph[vertex]: if i is 1 : l.append(c) c+=1 return l #the Bron-Kerbosch

Clique problem algorithm design

阅读更多关于 Clique problem algorithm design

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 Algorithm (in python-like pseudocode): def clique(A, k): P = A x A x A //Cartesian product for tuple in P:

Reduction to Clique prob

阅读更多关于 Reduction to Clique prob

Subgraph isomorphism We have the graphs G_1=(V_1,E_1), G_2=(V_2,E_2). Question : Is the graph G_1 isomorphic to a subgraph of G_2 ? (i.e. is there a subset of vertices of G_2, V ⊆ V_2 and subset of the edges of G_2, E ⊆ E_2 such that |V|=|V_1| and |E|=|E_1| and is there a one-to-one matching of the vertices of G_1 at the subset of vertices V of G_2, f:V_1 -> V such that {u,v} ∈ E_1 <=> { f(u),f(v) } ∈ E) Show that the problem Subgraph isomorphism belongs to NP. Show that the problem is NP-complete reducing the problem Clique to it. (Hint: consider that the graph G_1 is complete) I have tried