//#undef __FUNCT__
//#define __FUNCT__ "LowStretchSpanningTreeHelper"
void LowStretchSpanningTreeHelper(graph_t& g,const int root,const float alpha,
graph_t& h)//,int perm[])
{
int n,i,j,k;
std::vector<int> size,x,y;
std::vector<std::vector<int> > idx;
int ierr;
// PetscFunctionBegin;
weight_map_t edge_weight_g = get(edge_weight_t(),g);
// VertexWeight vertex_weight_h = get(vertex_weight_t(),h);
n = num_vertices(g);
if (n > 2) {
ierr = StarDecomp(g,root,1.0/3.0,alpha,k,size,idx,x,y);
j = 0;
for (i=1;i<=k;i++) {
graph_t& g1 = g.create_subgraph(idx[i].begin(),idx[i].end());
graph_t& h1 = h.create_subgraph(idx[i].begin(),idx[i].end());
LowStretchSpanningTreeHelper(g1,g1.global_to_local(g.local_to_global(x[i-1])),alpha,h1);//,perm+j);
j += size[i];
}
graph_t& g1 = g.create_subgraph(idx[0].begin(),idx[0].end());
graph_t& h1 = h.create_subgraph(idx[0].begin(),idx[0].end());
LowStretchSpanningTreeHelper(g1,g1.global_to_local(g.local_to_global(root)),alpha,h1);//,perm+j);
for (i=0;i<k;i++) {
float w = get(edge_weight_g,edge(x[i],y[i],g).first);
add_edge(x[i],y[i],w,h);
// put(vertex_weight_h,x[i],get(vertex_weight_h,x[i])+w);
// put(vertex_weight_h,y[i],get(vertex_weight_h,y[i])+w);
}
} else if (n == 2) {
graph_traits<graph_t>::edge_descriptor e = *(out_edges(root,g).first);
int t = target(e,g);
float w = get(edge_weight_g,e);
add_edge(root,t,w,h);
// put(vertex_weight_h,root,get(vertex_weight_h,root)+w);
// put(vertex_weight_h,t,get(vertex_weight_h,t)+w);
// perm[0] = g.local_to_global(t);
// perm[1] = g.local_to_global(root);
} else /* n == 1 */ {
// perm[0] = g.local_to_global(root);
}
//return 0;
}
//#undef __FUNCT__
//#define __FUNCT__ "LowStretchSpanningTreeHelper"
int StarDecomp(graph_t g,const int root,const float delta,const float epsilon,
int& k,std::vector<int>& size,std::vector<std::vector<int> >& idx,
std::vector<int>& x,std::vector<int>& y)
{
int n,m,edgesLeft;
//PetscErrorCode ierr;
//ShortestPathPriorityQueue pq;
// float radius;
std::vector<int> centerIdx;
//PQNode node;
// PetscFunctionBegin;
//printf("going to into ball cut segment\n");
graph_t& root_graph = g.is_root() ? g : g.root();
weight_map_t edge_weight_g = get(edge_weight,root_graph); // actually all property maps are same! so don't worry!
f_edges_t f_edges_g = get(edge_index, g);
vert_dist_t root_dist = get(vertex_distance, g);
n = num_vertices(g);
m = num_edges(g);
edgesLeft = m;
// std::vector<int>
// std::vector<int> pred(n,-1);
//std::vector<int> succ[n];
std::vector<int>::iterator i;
// float dist[n];
// std::vector<bool> taken(n,false);
// running dijkstra
float radius;
std::vector<vertex_descriptor> ordered_nodes(n);
int cntr = 0;
//std::vector<float> root_dist(n);
std::vector<int> pred(n, -1);
std::vector<int> color_map(n, WHITE);
//int num_root_edges = g.is_root() ? num_edges(g) : num_edges(g.root());
//printf("num_root_edges: %d\n", num_root_edges);
//std::vector<bool> fedges(num_root_edges);// turns out edge_index not local fedges(m, false);
p_comp_min_class comp(&root_dist);
identity_property_map ident;
PropertyMinQueue pq(n, comp, ident);
root_dist[root] = 0.0;
pred[root] = root;
pq.push(root);
//printf("about to go to dijkstra while loop\n");
while(!pq.empty())
{
//printf("top of while\n");
vertex_descriptor u = pq.top();
pq.pop();
color_map[u] = BLACK;
// put the edge that got us to u into fedges
vertex_descriptor pred_u = pred[u];
//radius = root_dist[u];
ordered_nodes[cntr++] = u;
if (pred_u != u)
{
edge_descriptor e = edge(pred_u, u, g).first;
put(f_edges_g, e, true);
}
//printf("after fedges\n");
adjacency_it i, i_end;
for (tie(i, i_end) = adjacent_vertices(u, g); i != i_end; i++)
{
vertex_descriptor v = *i;
if (color_map[v] == WHITE)
{
//printf("before pred[v]\n");
pred[v] = u;
//printf("before edge_weight_g; pred_u: %d, u: %d\n", pred_u, u);
root_dist[v] = root_dist[u] + 1.0/get(edge_weight_g, g.local_to_global(edge(u,v, g).first));
//printf("before color_map\n");
color_map[v] = GREY;
pq.push(v);
}
else if (color_map[v] == GREY)
{
float new_dist = root_dist[u] + 1.0/get(edge_weight_g, g.local_to_global(edge(u, v, g).first));
if (new_dist < root_dist[v])
{
root_dist[v] = new_dist;
pred[v] = u;
pq.update(v);
}
}
}
}
//printf("did dijkstra\n");
radius = root_dist[ordered_nodes.back()];
float min_radius = delta*radius;
int center_size = 0;
float boundary = 0.0;
int edge_count = 0;
// repurpose color_map to tell whether nodes are in ball or not
color_map.clear(); // does clear cause mem alloc slowness
// root_dist.clear();
//color_map.resize(n, WHITE);
std::vector<int> partition_map(n, -1); // -1: not in a partition yet , 0 -> n: the partion number (0= center ball)
int cur_part = 0;
while (root_dist[ordered_nodes[center_size]] < min_radius
|| boundary > (edge_count+1)*log(m)/(log(2.0)*(1.0-2.0*delta)*radius))
{
vertex_descriptor u = ordered_nodes[center_size++];
partition_map[u] = cur_part;
centerIdx.push_back(g.local_to_global(u));
adjacency_it i, i_end;
for (tie(i, i_end) = adjacent_vertices(u, g); i != i_end; i++)
{
vertex_descriptor v = *i;
if (partition_map[v] != cur_part)
{
edge_count++;
boundary += get(edge_weight_g, g.local_to_global(edge(u,v,g).first));
}
else
boundary -= get(edge_weight_g, g.local_to_global(edge(u,v,g).first));
}
}
size.push_back(centerIdx.size());
idx.push_back(centerIdx);
// NOTE we found center region but have not done anything about returning it yet!
// center region should now just be the first center_size nodes in ordered_nodes
// find "shell" around ball that make up potential anchor
std::queue<vertex_descriptor> anchor_q;
for (int i = center_size; i < n; i++)
{
vertex_descriptor u = ordered_nodes[i];
adjacency_it neighbor_i, neighbor_end;
for (tie(neighbor_i, neighbor_end) = adjacent_vertices(u, g); neighbor_i != neighbor_end; neighbor_i++)
{
vertex_descriptor v = *neighbor_i;
if (partition_map[v] == cur_part)
{
anchor_q.push(u);
break;
}
}
}
//printf("done with ball cut segment\n");
// now we make cones
while (!anchor_q.empty())
{
vertex_descriptor anchor = anchor_q.front();
anchor_q.pop();
if (partition_map[anchor] >= 0) // have we already included node in new cone
continue;
cur_part++; // cones numbered 1,2,3,...
std::vector<int> cone_idx;
std::vector<int> cone_color_map(n, WHITE);
//std::vector<float> cone_dist(n);
vert_dist_t cone_dist = get(vertex_distance, g);
//std::vector<vertex_descriptor> cone_ordered_nodes(n);
int cone_edge_count = 0;
int cone_internal_edge_count = 0;
float cone_boundary = 0.0;
p_comp_min_class cone_comp(&cone_dist);
//identity_property_map cone_ident;
PropertyMinQueue cone_pq(n, cone_comp, ident);
cone_dist[anchor] = 0.0;
cone_color_map[anchor] = GREY;
cone_pq.push(anchor);
//int node_cntr = 0;
bool initialized_cone = false; // i.e. have we included all nodes within dist 0.0
float cone_r = 0.0;
float init_r_limit = 0.0;
float boundary_limit = 0.0;
while (!cone_pq.empty())
{
vertex_descriptor u = cone_pq.top();
float new_r = cone_dist[u];
if (!initialized_cone && new_r > init_r_limit + SMIDGEN)
{
initialized_cone = true;
if (cone_edge_count == 0)
boundary_limit = log(m+1)*2.0/(log(2.0) * epsilon);
else
boundary_limit = cone_edge_count * log(m / cone_internal_edge_count) / (log(2.0) * epsilon); // (edgeCount)*log(edgesLeft*1.0/initialInternalConeEdges)*2.0/(log(2.0)*epsilon*radius))
}
if (initialized_cone
&& new_r > cone_r + SMIDGEN
&& cone_boundary <= boundary_limit)
break;
cone_r = new_r;
cone_pq.pop();
cone_color_map[u] = BLACK;
partition_map[u] = cur_part;
cone_idx.push_back(g.local_to_global(u));
adjacency_it i, i_end;
for (tie(i, i_end) = adjacent_vertices(u, g); i != i_end; i++)
{
// calculate boundary/volume props
vertex_descriptor v = *i;
if (partition_map[v] != cur_part)
{
cone_edge_count++;
cone_boundary += get(edge_weight_g, g.local_to_global(edge(u,v,g).first));
}
else
{
cone_boundary -= get(edge_weight_g, g.local_to_global(edge(u,v,g).first));
cone_internal_edge_count++;
}
// consider more nodes
if (partition_map[v] < 0)
{
//int e_local_index = get(edge_index_g, g.global_to_local(edge(u,v,g).first));
//int e_index = get(edge_index_g, edge(u,v,g).first);
//printf("e_index:%d num_edges:%d num_edges_root:%d \n", num_edges(g), num_edges(g.root()));
if (cone_color_map[v] == WHITE
&& get(f_edges_g, edge(u,v,g).first))
{
cone_color_map[v] = GREY;
cone_dist[v] = cone_dist[u];
cone_pq.push(v);
}
else if (cone_color_map[v] == WHITE
&& !get(f_edges_g, edge(u,v,g).first))
{
cone_color_map[v] = GREY;
cone_dist[v] = cone_dist[u] + get(edge_weight_g, g.local_to_global(edge(u,v,g).first));
cone_pq.push(v);
}
else if (cone_color_map[v] == GREY
&& get(f_edges_g, edge(u,v,g).first))
{
float new_dist = cone_dist[u]; // note this should always be at least as small as old dist
if (new_dist < cone_dist[v])
{
cone_dist[v] = new_dist;
cone_pq.update(v);
}
}
else if (cone_color_map[v] == GREY
&& !get(f_edges_g, edge(u,v,g).first))
{
float new_dist = cone_dist[u] + get(edge_weight_g, g.local_to_global(edge(u,v,g).first));
if (new_dist < cone_dist[v])
{
cone_dist[v] = new_dist;
cone_pq.update(v);
}
}
}
}
}
x.push_back(anchor);
y.push_back(pred[anchor]);
size.push_back(cone_idx.size());
idx.push_back(cone_idx);
}
k = cur_part;
// still have to pass back the new partionings etc.
// /** form tree of shortest paths to root **/
// graph_traits<graph_t>::out_edge_iterator e, e_end;
// for (tie(e,e_end)=out_edges(root,g); e!=e_end; e++) {
// int t = target(*e,g);
// pq.push(PQNode(t,root,1.0/get(edge_weight_g,*e)));
// }
// pred[root] = root;
// while (!pq.empty()) {
// node = pq.top();pq.pop();
// if (pred[node.vertex] == -1) {
// succ[node.pred].push_back(node.vertex);
// pred[node.vertex] = node.pred;
// dist[node.vertex] = node.dist;
// for (tie(e,e_end)=out_edges(node.vertex,g); e!=e_end; e++) {
// int t = target(*e,g);
// if (pred[t] == -1) {
// pq.push(PQNode(t,node.vertex,node.dist+1.0/get(edge_weight_g,*e)));
// }
// }
// radius = node.dist;
// }
// }
// /** BALL CUT **/
// for (i=succ[root].begin();i!=succ[root].end();i++) {
// pq.push(PQNode(*i,dist[*i]));
// }
// float boundary = 0;
// int edgeCount = 0; // all edges not just edges on boundary?
// centerIdx.push_back(g.local_to_global(root));
// taken[root] = true;//PETSC_TRUE;
// centerSize = 1;
// for (tie(e,e_end)=out_edges(root,g); e!=e_end; e++) {
// boundary += get(edge_weight_g,*e);
// edgeCount++;
// }
// const float minRadius = delta*radius;
// while (dist[pq.top().vertex] < minRadius) {
// assert(!pq.empty());
// node = pq.top();pq.pop();
// centerIdx.push_back(g.local_to_global(node.vertex));
// taken[node.vertex] = true;//PETSC_TRUE;
// centerSize++;
// for (tie(e,e_end)=out_edges(node.vertex,g); e!=e_end; e++) {
// if (taken[target(*e,g)]) {
// boundary -= get(edge_weight_g,*e);
// } else {
// boundary += get(edge_weight_g,*e);
// edgeCount++;
// }
// }
// for (i=succ[node.vertex].begin();i!=succ[node.vertex].end();i++) {
// pq.push(PQNode(*i,dist[*i]));
// }
// }
// while (boundary > (edgeCount+1)*log(m)/(log(2)*(1-2*delta)*radius)) {
// assert(!pq.empty());
// node = pq.top();pq.pop();
// centerIdx.push_back(g.local_to_global(node.vertex));
// taken[node.vertex] = true;//PETSC_TRUE;
// centerSize++;
// for (tie(e,e_end)=out_edges(node.vertex,g); e!=e_end; e++) {
// if (taken[target(*e,g)]) {
// boundary -= get(edge_weight_g,*e);
// } else {
// boundary += get(edge_weight_g,*e);
// edgeCount++;
// }
// }
// for (i=succ[node.vertex].begin();i!=succ[node.vertex].end();i++) {
// pq.push(PQNode(*i,dist[*i]));
// }
// }
// size.push_back(centerSize);
// idx.push_back(centerIdx);
// edgesLeft -= edgeCount;
// k = 0;
// assert(!pq.empty());
// std::queue<int> anchor_q;
// ShortestPathPriorityQueue cone_pq;
// std::vector<int> cone_succ[n];
// std::vector<bool> cone_found(n,false);//PETSC_FALSE);
// /** form tree of shortest paths to an anchor **/
// while (!pq.empty()) {
// node = pq.top();pq.pop();
// cone_found[node.vertex] = true;//PETSC_TRUE;
// anchor_q.push(node.vertex);
// for (tie(e,e_end)=out_edges(node.vertex,g); e!=e_end; e++) {
// int t = target(*e,g);
// if (!taken[t]) {
// cone_pq.push(PQNode(t,node.vertex,1.0/get(edge_weight_g,*e)));
// }
// }
// }
// while (!cone_pq.empty()) {
// node = cone_pq.top();cone_pq.pop();
// if (!cone_found[node.vertex]) {
// cone_succ[node.pred].push_back(node.vertex);
// cone_found[node.vertex] = true;//PETSC_TRUE;
// for (tie(e,e_end)=out_edges(node.vertex,g); e!=e_end; e++) {
// int t = target(*e,g);
// if (!taken[t] && !cone_found[t]) {
// cone_pq.push(PQNode(t,node.vertex,node.dist+1.0/get(edge_weight_g,*e)));
// }
// }
// }
// }
// while (!anchor_q.empty()) {
// /** CONE CUT **/
// int anchor = anchor_q.front();anchor_q.pop();
// if (!taken[anchor]) {
// int v;
// int thisSize = 0;
// std::vector<int> thisIdx;
// std::queue<int> q;
// ShortestPathPriorityQueue mycone_pq;
// std::vector<bool> mycone_taken(n,false);//);PETSC_FALSE);
// int initialInternalConeEdges = 0;
// boundary = 0;
// edgeCount = 0;
// q.push(anchor);
// while (!q.empty()) {
// v = q.front();q.pop();
// taken[v] = true;//PETSC_TRUE;
// mycone_taken[v] = true;//PETSC_TRUE;
// thisIdx.push_back(g.local_to_global(v));
// thisSize++;
// for (i=cone_succ[v].begin();i!=cone_succ[v].end();i++) {
// q.push(*i);
// }
// for (tie(e,e_end)=out_edges(v,g); e!=e_end; e++) {
// int t = target(*e,g);
// if (!taken[t]) {
// mycone_pq.push(PQNode(t,v,1.0/get(edge_weight_g,*e)));
// boundary += get(edge_weight_g,*e);
// edgeCount++;
// } else if (mycone_taken[t]) {
// boundary -= get(edge_weight_g,*e);
// initialInternalConeEdges++;
// }
// }
// }
// if (initialInternalConeEdges < edgesLeft) {
// while (initialInternalConeEdges == 0 ?
// boundary > (edgeCount+1)*log(edgesLeft+1)*2.0/(log(2.0)*epsilon*radius) :
// boundary > (edgeCount)*log(edgesLeft*1.0/initialInternalConeEdges)*2.0/(log(2.0)*epsilon*radius))
// {
// assert(!mycone_pq.empty());
// node = mycone_pq.top();mycone_pq.pop();
// if (!mycone_taken[node.vertex]) {
// q.push(node.vertex);
// while (!q.empty()) {
// v = q.front();q.pop();
// taken[v] = true;//PETSC_TRUE;
// mycone_taken[v] = true;//PETSC_TRUE;
// thisIdx.push_back(g.local_to_global(v));
// thisSize++;
// for (i=cone_succ[v].begin();i!=cone_succ[v].end();i++) {
// q.push(*i);
// }
// for (tie(e,e_end)=out_edges(v,g); e!=e_end; e++) {
// int t = target(*e,g);
// if (!taken[t]) {
// mycone_pq.push(PQNode(t,v,node.dist+1.0/get(edge_weight_g,*e)));
// boundary += get(edge_weight_g,*e);
// edgeCount++;
// } else if (mycone_taken[t]) {
// boundary -= get(edge_weight_g,*e);
// }
// }
// }
// }
// }
// }
// edgesLeft -= edgeCount;
// size.push_back(thisSize);
// idx.push_back(thisIdx);
// x.push_back(anchor);
// y.push_back(pred[anchor]);
// k++;
// }
// }
// /*
// // pseudo cone cut
// while (!pq.empty()) {
// node = pq.top();pq.pop();
// PetscInt thisSize = 1;
// std::vector<PetscInt> thisIdx;
// std::queue<PetscInt> q;
// thisIdx.push_back(g.local_to_global(node.vertex));
// for (i=succ[node.vertex].begin();i!=succ[node.vertex].end();i++) {
// q.push(*i);
// }
// PetscInt v;
// while (!q.empty()) {
// v = q.front();q.pop();
// thisSize++;
// thisIdx.push_back(g.local_to_global(v));
// for (i=succ[v].begin();i!=succ[v].end();i++) {
// q.push(*i);
// }
// }
// size.push_back(thisSize);
// idx.push_back(thisIdx);
// x.push_back(node.vertex);
// y.push_back(pred[node.vertex]);
// k++;
// }
// */
return 0;
}
