I'm writing a brute-force algorithm to solve vertex cover like this:
BruteForceVertexCover( Graph G = (V,E) ){
for size= 1 ... |V|
vector<int> v = {0...size-1}
do{
if(test(G, v)) return v; //test if v covers G
}
while(v has next combinations of lenght size);
return empty vector<int>;
}
//this stops when find a answer, and it will find,
//since it tries all combinations of all sizes
where
bool test( Graph G = (V,E), vector<int> v ){
for each u in v:
for each w in G[u]
remove u from G[w] //this is linear in size of vector G[w]
clear G[v] //removed all (bidirectional) edges that have u
for i = 0 ... |V|
if(G[i] is not empty) return false;
return true;
}
im trying this to lots of graphs (but their maximum size is 20 vertices) and this is taking a decade... is there any optimization I can do on this brute force so it run faster?