clique-problem

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

由 牧云@^-^@ 提交于 2020-01-02 01:20:12
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

由 陌路散爱 提交于 2019-12-31 10:44:12
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

由 旧巷老猫 提交于 2019-12-25 18:24:25
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

由 眉间皱痕 提交于 2019-12-19 10:42:49
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

由 爱⌒轻易说出口 提交于 2019-12-19 10:42:11
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

Implementing Bron–Kerbosch algorithm in python

由 旧巷老猫 提交于 2019-12-12 08:15:11
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

由 老子叫甜甜 提交于 2019-12-03 16:14:44
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

由 ♀尐吖头ヾ 提交于 2019-12-02 23:53:07
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

由 家住魔仙堡 提交于 2019-12-01 11:44:20
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
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