int buildTreeWidthDecomposition(Graph& g, GenericTree& twd, vector<set<int> >& nodedirectory){//return the max_bag_size of this decomposition
set<VertexDegreePair,VertexDegreePairComp> DegreeRank;//first is degree; second is vertex id;
vector<int> DegreeList(g.num_vertices(),0);
int max_bag_size=-1;
for(int i=0; i<g.num_vertices(); i++){
int current_degree=g.get_degree(i);
DegreeRank.insert(VertexDegreePair(i, current_degree));
DegreeList[i]=current_degree;
}
while(DegreeRank.size()>0){
set<VertexDegreePair,VertexDegreePairComp>::iterator minDegreeVertex=DegreeRank.begin();
DegreeRank.erase(DegreeRank.begin());
int current_vertexID=minDegreeVertex->first;
//build treenode
nodedirectory.push_back(set<int>());
int current_nodeID=nodedirectory.size()-1;
nodedirectory.back().insert(current_vertexID);
for(EdgeList::iterator vit=g.get_neighbors(current_vertexID).begin(); vit<g.get_neighbors(current_vertexID).end(); vit++){
nodedirectory.back().insert(*vit);
g[*vit].nodes.push_back(current_nodeID);
//update on graph
EdgeList::iterator iit=g.get_neighbors(current_vertexID).begin();
EdgeList::iterator jit=g.get_neighbors(*vit).begin();
EdgeList combined;
while(iit<g.get_neighbors(current_vertexID).end() && jit<g.get_neighbors(*vit).end()){
//It is assumed that a vertex itself does not appear in its adjacent list and the adjacent list is in ascending order.
if(*iit==*vit){
iit++;
continue;
}else if (*jit==current_vertexID){
jit++;
continue;
}
if(*iit<*jit){
combined.push_back(*iit);
iit++;
}else if(*iit>*jit){
combined.push_back(*jit);
jit++;
}else{//implies *iit==*jit
combined.push_back(*iit);
iit++;
jit++;
}
}
if(iit<g.get_neighbors(current_vertexID).end() && jit<g.get_neighbors(*vit).end()){
cout<<"Internal Logic Error. Exit."<<endl;
exit(-1);
}
for(; iit<g.get_neighbors(current_vertexID).end(); iit++){
if(*iit!=*vit)
combined.push_back(*iit);
}
for(; jit<g.get_neighbors(*vit).end(); jit++){
if(*jit!=current_vertexID)
combined.push_back(*jit);
}
g.get_neighbors(*vit)=combined;
//update on graph done
//update on nodes
vector<int> reduced;
vector<int>::iterator itern=g[*vit].nodes.begin();
vector<int>::iterator jtern=g[current_vertexID].nodes.begin();
while(itern<g[*vit].nodes.end() && jtern<g[current_vertexID].nodes.end()){
if(*itern<*jtern){
reduced.push_back(*itern);
itern++;
}
else if (*itern>*jtern){
jtern++;
}
else{//implies *itern==*jtern
itern++;
jtern++;
}
}
for(; itern<g[*vit].nodes.end(); itern++)
reduced.push_back(*itern);
g[*vit].nodes=reduced;
//update on nodes done
//other update
set<VertexDegreePair,VertexDegreePairComp>::iterator fit=DegreeRank.find(VertexDegreePair(*vit, DegreeList[*vit]));
DegreeRank.erase(fit);
DegreeRank.insert(VertexDegreePair(*vit, g.get_degree(*vit)));
DegreeList[*vit]=g.get_degree(*vit);
//other update done
}
max_bag_size=int(nodedirectory.back().size())>max_bag_size? int(nodedirectory.back().size()) : max_bag_size;
//build treenode done
//build decomposition tree
twd.addNode(twd.num_nodes());
for(vector<int>::iterator nit=g[current_vertexID].nodes.begin(); nit<g[current_vertexID].nodes.end(); nit++){
twd.addEdge(current_nodeID, *nit);//current_nodeID shall always be larger than *nit;
twd.addEdge(*nit, current_nodeID);
}
//build decomposition tree done
//clear deleted vertex
g[current_vertexID].nodes.clear();
g.get_neighbors(current_vertexID).clear();
//clear deleted vertex
}
return max_bag_size;
}
