private void augment(Vertex a, Dictionary <Vertex, Boolean> free,
Dictionary <Vertex, Edge> pred, Dictionary <Vertex, Int32> dist,
Dictionary <Vertex, Int32> pot, FibHeap PQ)
{
//init
//dist from a is zero
dist[a] = 0;
//a is the best vertex in A
Vertex bestVertexInA = a;
//potential of a
int minA = pot[a];
int delta;
//make a stack for nodes in A that are visited during the shortest path comp.
Stack <Vertex> RA = new Stack <Vertex>();
RA.Push(a);
//make a strack for the nodes in B that are visited during the shortest path comp.
Stack <Vertex> RB = new Stack <Vertex>();
Vertex a1 = a;
//relax all edges out of a1
List <Edge> adjEdges = a1.getAdjList();
if (adjEdges == null)
{
return;
}
foreach (Edge e in adjEdges)
{
Vertex b = e.getTarget();
//set the distance from a1 to all its neighbors.
int db = dist[a1] + (pot[a1] + pot[b] - e.getCost());
dist[b] = db;
pred[b] = e; //predecessor for b is e
RB.Push(b); //push to stack
PQ.insert(b, db); //insert in priority queue
}
//select from PQ the vertex b with min distance db
while (true)
{
Vertex b;
int db = 0;
if (PQ.empty())
{
b = null;
}
else
{
b = (Vertex)PQ.extractMin();
db = dist[b];
}
//distinguish three cases
if (b == null || db >= minA)
{
//We have a node v in A with potential zero. augment a path from a to v.
delta = minA;
//augmentation by path to best vertex in A
augmentPathTo(bestVertexInA, pred);
free[a] = false;
free[bestVertexInA] = true;
break;
}
else
{
//b is a free node, can be matched
if (free[b])
{
delta = db;
//augmentation by path to b
augmentPathTo(b, pred);
free[a] = false;
free[b] = false;
break;
}
//Neither of the above. b is matched
else
{
//continue shortest-path computation
Edge e = b.getFirstAdjEdge();
a1 = e.getTarget(); //target of b
pred[a1] = e;
RA.Push(a1);
dist[a1] = db;
//if better than minA
if ((db + pot[a1]) < minA)
{
bestVertexInA = a1;
minA = db + pot[a1];
}
//relax all edges out of a1
adjEdges = a1.getAdjList();
foreach (Edge e1 in adjEdges)
{
b = e1.getTarget();
db = dist[a1] + (pot[a1] + pot[b] - e1.getCost());
if (pred[b] == null)
{
dist[b] = db;
pred[b] = e1;
RB.Push(b);
PQ.insert(b, db);
}
//b is already in the priority queue
else
{
if (db < dist[b])
{
dist[b] = db;
pred[b] = e1;
PQ.decreaseKey(b, db);
}
}
}
}
}
}
//augment: potential update and reinit
//Update the potential and remove the nodes from the stack
while (RA.Count > 0)
{
Vertex tmp = RA.Pop();
pred[tmp] = null;
int potChange = delta - dist[tmp];
if (potChange <= 0)
{
continue;
}
pot[tmp] = (pot[tmp] - potChange);
}
//Update the potential and remove the nodes from the stack.
while (RB.Count > 0)
{
Vertex tmp = RB.Pop();
pred[tmp] = (Edge)null;
//if b is in the heap
if (PQ.member(tmp))
{
PQ.delete(tmp);
}
int potChange = delta - dist[tmp];
if (potChange <= 0)
{
continue;
}
pot[tmp] = (pot[tmp] + potChange);
}
}
private void augment(Vertex a, Dictionary<Vertex, Boolean> free,
Dictionary<Vertex, Edge> pred, Dictionary<Vertex, Int32> dist,
Dictionary<Vertex, Int32> pot, FibHeap PQ)
{
//init
//dist from a is zero
dist[a] = 0;
//a is the best vertex in A
Vertex bestVertexInA = a;
//potential of a
int minA = pot[a];
int delta;
//make a stack for nodes in A that are visited during the shortest path comp.
Stack<Vertex> RA = new Stack<Vertex>();
RA.Push(a);
//make a strack for the nodes in B that are visited during the shortest path comp.
Stack<Vertex> RB = new Stack<Vertex>();
Vertex a1 = a;
//relax all edges out of a1
List<Edge> adjEdges = a1.getAdjList();
if(adjEdges == null)
return;
foreach(Edge e in adjEdges){
Vertex b = e.getTarget();
//set the distance from a1 to all its neighbors.
int db = dist[a1] + (pot[a1] + pot[b] - e.getCost());
dist[b] = db;
pred[b] = e; //predecessor for b is e
RB.Push(b); //push to stack
PQ.insert(b, db); //insert in priority queue
}
//select from PQ the vertex b with min distance db
while(true){
Vertex b;
int db = 0;
if(PQ.empty()){
b = null;
}
else {
b = (Vertex) PQ.extractMin();
db = dist[b];
}
//distinguish three cases
if(b == null || db >= minA){
//We have a node v in A with potential zero. augment a path from a to v.
delta = minA;
//augmentation by path to best vertex in A
augmentPathTo(bestVertexInA, pred);
free[a] = false;
free[bestVertexInA] = true;
break;
}
else {
//b is a free node, can be matched
if(free[b]){
delta = db;
//augmentation by path to b
augmentPathTo(b, pred);
free[a] = false;
free[b] = false;
break;
}
//Neither of the above. b is matched
else {
//continue shortest-path computation
Edge e = b.getFirstAdjEdge();
a1 = e.getTarget(); //target of b
pred[a1] = e;
RA.Push(a1);
dist[a1] = db;
//if better than minA
if((db + pot[a1]) < minA){
bestVertexInA = a1;
minA = db + pot[a1];
}
//relax all edges out of a1
adjEdges = a1.getAdjList();
foreach(Edge e1 in adjEdges){
b = e1.getTarget();
db = dist[a1] + (pot[a1] + pot[b] - e1.getCost());
if(pred[b] == null){
dist[b] = db;
pred[b] = e1;
RB.Push(b);
PQ.insert(b, db);
}
//b is already in the priority queue
else {
if(db < dist[b]){
dist[b] = db;
pred[b] = e1;
PQ.decreaseKey(b, db);
}
}
}
}
}
}
//augment: potential update and reinit
//Update the potential and remove the nodes from the stack
while(RA.Count > 0){
Vertex tmp = RA.Pop();
pred[tmp] = null;
int potChange = delta - dist[tmp];
if(potChange <= 0){
continue;
}
pot[tmp] = (pot[tmp] - potChange);
}
//Update the potential and remove the nodes from the stack.
while(RB.Count > 0){
Vertex tmp = RB.Pop();
pred[tmp] = (Edge) null;
//if b is in the heap
if(PQ.member(tmp)){
PQ.delete(tmp);
}
int potChange = delta - dist[tmp];
if(potChange <= 0){
continue;
}
pot[tmp] = (pot[tmp] + potChange);
}
}
public List <Edge> maxWeightBipartiteMatching(List <Vertex> A, List <Vertex> B, List <Edge> edges, int p, int q)
{
//Init
//Each node is either free = true or matched = false
Dictionary <Vertex, Boolean> free = new Dictionary <Vertex, Boolean>(p + q);
//Both these data structures are used in the shortest path computation
//The predecessor edge of a vertex. Either an edge or null
Dictionary <Vertex, Edge> pred = new Dictionary <Vertex, Edge>(p + q);
//The distance to this vertex
Dictionary <Vertex, Int32> dist = new Dictionary <Vertex, Int32>(p + q);
//The potential of this vertex. Cf. the book for more information
Dictionary <Vertex, Int32> pot = new Dictionary <Vertex, Int32>(p + q);
//For all vertices in A and B
foreach (Vertex a in A)
{
free.Add(a, true); //a is free.
pred.Add(a, (Edge)null); //No predecessor
dist.Add(a, 0); //distance is zero
pot.Add(a, 0); //potential is zero
}
foreach (Vertex b in B)
{
free.Add(b, true);
pred.Add(b, (Edge)null);
dist.Add(b, 0);
pot.Add(b, 0);
}
//List for the edges that are part of the max weight bip. matching
List <Edge> result = new List <Edge>(q);
FibHeap PQ = new FibHeap(q);
//Naive heuristic used to set the potential of the vertices in A
int C = 0;
//Find the edge with the heaviest cost
foreach (Edge e in edges)
{
if (e.getCost() > C)
{
C = e.getCost();
}
}
//Set the potential to all vertices in A to the heaviest cost
foreach (Vertex a in A)
{
pot[a] = C;
}
//Augment from all vertices in A
foreach (Vertex a in A)
{
if (free[a])
{
augment(a, free, pred, dist, pot, PQ);
}
}
foreach (Vertex b in B)
{
//add all out edges from b (these are the matching edges. all matching edges goes from B to A)
Edge e = b.getFirstAdjEdge();
if (e != null)
{
result.Add(e);
}
}
//All edges that are part of the max bip. weight matching goes from B to A. We therefore need to reverse them.
foreach (Edge e in result)
{
e.reverseEdge();
}
return(result);
}
public List<Edge> maxWeightBipartiteMatching(List<Vertex> A, List<Vertex> B, List<Edge> edges, int p, int q)
{
//Init
//Each node is either free = true or matched = false
Dictionary<Vertex, Boolean> free = new Dictionary<Vertex, Boolean>(p + q);
//Both these data structures are used in the shortest path computation
//The predecessor edge of a vertex. Either an edge or null
Dictionary<Vertex, Edge> pred = new Dictionary<Vertex, Edge>(p + q);
//The distance to this vertex
Dictionary<Vertex, Int32> dist = new Dictionary<Vertex, Int32>(p + q);
//The potential of this vertex. Cf. the book for more information
Dictionary<Vertex, Int32> pot = new Dictionary<Vertex, Int32>(p + q);
//For all vertices in A and B
foreach (Vertex a in A)
{
free.Add(a, true); //a is free.
pred.Add(a, (Edge)null); //No predecessor
dist.Add(a, 0); //distance is zero
pot.Add(a, 0); //potential is zero
}
foreach (Vertex b in B)
{
free.Add(b, true);
pred.Add(b, (Edge)null);
dist.Add(b, 0);
pot.Add(b, 0);
}
//List for the edges that are part of the max weight bip. matching
List<Edge> result = new List<Edge>(q);
FibHeap PQ = new FibHeap(q);
//Naive heuristic used to set the potential of the vertices in A
int C = 0;
//Find the edge with the heaviest cost
foreach (Edge e in edges)
{
if (e.getCost() > C)
{
C = e.getCost();
}
}
//Set the potential to all vertices in A to the heaviest cost
foreach (Vertex a in A)
{
pot[a] = C;
}
//Augment from all vertices in A
foreach (Vertex a in A)
{
if (free[a])
{
augment(a, free, pred, dist, pot, PQ);
}
}
foreach (Vertex b in B)
{
//add all out edges from b (these are the matching edges. all matching edges goes from B to A)
Edge e = b.getFirstAdjEdge();
if (e != null)
{
result.Add(e);
}
}
//All edges that are part of the max bip. weight matching goes from B to A. We therefore need to reverse them.
foreach (Edge e in result)
{
e.reverseEdge();
}
return result;
}