//A quadratic interger program for graph matching,
//When tuned with the right similarity function it can represent the GED problem.
// See Pattern Reocgnition Paper paper On the unification of graph matching and graph edit distance paper.
//The directed version has not been tested yet
public override void QAPGMGED()
{
//some important variables
int nbNode1 = graph1.ListNodes.Count;
int nbNode2 = graph2.ListNodes.Count;
int nbvar = nbNode1 * nbNode2; // number of variables
int nbcontraintes = nbNode1 + nbNode2; // number of constraints
Graphs.Label nodeepslabel;
//Adjacency matrices
MatrixLibrary.Matrix adj1 = graph1.calculateAdjacencyMatrix();
MatrixLibrary.Matrix adj2 = graph2.calculateAdjacencyMatrix();
//Similarity matrix
Double[,] S = new Double[nbvar, nbvar];
//Creation of the Similarity matrix
//4 for loops integrated
int countrow = -1;
for (int i = 0; i < nbNode1; i++)
{
Node nodei = graph1.ListNodes[i];
for (int k = 0; k < nbNode2; k++)
{
Node nodek = graph2.ListNodes[k];
countrow = countrow + 1;
int countcol = -1;
for (int j = 0; j < nbNode1; j++)
{
Node nodej = graph1.ListNodes[j];
for (int l = 0; l < nbNode2; l++)
{
Node nodel = graph2.ListNodes[l];
countcol = countcol + 1;
if (i == j && k == l) // Similarity between nodes
{
Type typeLabel = nodei.Label.GetType();
object obj = Activator.CreateInstance(typeLabel);
nodeepslabel = (Graphs.Label)obj;
nodeepslabel.Id = ConstantsAC.EPS_ID;
double costsub = nodei.Label.dissimilarity(nodek.Label);
double costdel = nodei.Label.dissimilarity(nodeepslabel);
double costins = nodeepslabel.dissimilarity(nodek.Label);
double cost = costsub - costdel - costins;
cost *= -1;
S[countrow, countcol] = cost;
}
else // Similarity between edges
{
int connect1 = (int)adj1[i, j];
int connect2 = (int)adj2[k, l];
if (connect1 == 1 && connect2 == 1) // Two edges are connected
{
Edge ij = findedge(nodei, nodej);
Edge kl = findedge(nodek, nodel);
Type typeLabel = ij.Label.GetType();
object obj = Activator.CreateInstance(typeLabel);
nodeepslabel = (Graphs.Label)obj;
nodeepslabel.Id = ConstantsAC.EPS_ID;
double costsub = ij.Label.dissimilarity(kl.Label);
double costdel = ij.Label.dissimilarity(nodeepslabel);
double costins = nodeepslabel.dissimilarity(kl.Label);
double cost = costsub - costdel - costins;
cost *= -1;
//cost *= 0.5;
S[countrow, countcol] = cost;
}
}
}
}
}
}
//We compute the constant that represents the
//deletion and insertion of the nodes and edges
//deletions of the nodes of g1
double constante = 0;
for (int i = 1; i <= nbNode1; i++)
{
Type typeLabel = graph1.ListNodes[i - 1].Label.GetType();
object obj = Activator.CreateInstance(typeLabel);
nodeepslabel = (Graphs.Label)obj;
nodeepslabel.Id = ConstantsAC.EPS_ID;
constante += (graph1.ListNodes[i - 1].Label).dissimilarity(nodeepslabel);
}
//deletions of the edges of g1
for (int ij = 1; ij <= nbEdge1; ij++)
{
Type typeLabel = graph1.ListEdges[ij - 1].Label.GetType();
object obj = Activator.CreateInstance(typeLabel);
nodeepslabel = (Graphs.Label)obj;
nodeepslabel.Id = ConstantsAC.EPS_ID;
double costEdge = (graph1.ListEdges[ij - 1].Label).dissimilarity(nodeepslabel);
constante += costEdge;
}
//insertions of the nodes of g2
for (int k = 1; k <= nbNode2; k++)
{
Type typeLabel = graph2.ListNodes[k - 1].Label.GetType();
object obj = Activator.CreateInstance(typeLabel);
nodeepslabel = (Graphs.Label)obj;
nodeepslabel.Id = ConstantsAC.EPS_ID;
constante += (graph2.ListNodes[k - 1].Label).dissimilarity(nodeepslabel);
}
//insertions of the edges of g2
for (int kl = 1; kl <= nbEdge2; kl++)
{
Type typeLabel = graph2.ListEdges[kl - 1].Label.GetType();
object obj = Activator.CreateInstance(typeLabel);
nodeepslabel = (Graphs.Label)obj;
nodeepslabel.Id = ConstantsAC.EPS_ID;
double costEdge = (graph2.ListEdges[kl - 1].Label).dissimilarity(nodeepslabel);
constante += costEdge;
}
// the number of variables is the number of columns
int nbCols = nbvar;
// the number of constraints is the number of rows
int nbRows = nbcontraintes;
List <string> colNameList = new List <string>();
//We create the name of the vrariables for all couples of nodes in g1 and g2
for (int i = 0; i < nbNode1; i++)
{
for (int k = 0; k < nbNode2; k++)
{
colNameList.Add("x_" + graph1.ListNodes[i].Id + "," + graph2.ListNodes[k].Id + "");
}
}
try
{
cplex = new Cplex(); // creation du modèle CPLEX
this.ilpMatrix = cplex.AddLPMatrix(); // matrice du pb (initialisée à 0 colonnes et 0 lignes)
ColumnArray colonnes = cplex.ColumnArray(ilpMatrix, nbCols); // définition des variables-colonnes du pb
// ajout des variables-colonnes dans la matrice du pb
// y is a vector
INumVar[] y = cplex.NumVarArray(colonnes, 0, 1, NumVarType.Bool, colNameList.ToArray());
#region création fonction objectif
// CALCUL DES COEFFICIENTS
// We create the ojective function
INumExpr[] coeffs_expr = new INumExpr[nbvar * nbvar]; // vecteur des coeffs des coûts des arrêtes
int count = 0;
for (int ik = 0; ik < nbvar; ik++)
{
for (int jl = 0; jl < nbvar; jl++)
{
coeffs_expr[count] = cplex.Prod(y[ik], y[jl]);
coeffs_expr[count] = cplex.Prod(S[ik, jl], coeffs_expr[count]);
count = count + 1;
}
}
INumExpr ff = cplex.Sum(coeffs_expr);
INumExpr gg = cplex.Sum(ff, cplex.Constant(-constante));
cplex.AddMaximize(gg);
#endregion
#region définition des contraintes du pb
// We create the constraints
// The sum of x variables by rows
for (int i = 0; i < nbNode1; i++)
{
INumVar[] sommeLignes = new INumVar[nbNode2];
for (int k = 0; k < nbNode2; k++)
{
string nameVarik = "x_" + i + "," + k;
int indexik = SolverCPLEX.GetIndexByName(y, nameVarik);
sommeLignes[k] = y[indexik];
}
cplex.AddLe(cplex.Sum(sommeLignes), 1);
}
// The sum of x variables by columns
for (int k = 0; k < nbNode2; k++)
{
INumVar[] sommeLignes = new INumVar[nbNode1];
for (int i = 0; i < nbNode1; i++)
{
string nameVarik = "x_" + i + "," + k;
int indexik = SolverCPLEX.GetIndexByName(y, nameVarik);
sommeLignes[i] = y[indexik];
}
cplex.AddLe(cplex.Sum(sommeLignes), 1);
}
#endregion
}
catch (ILOG.Concert.Exception e)
{
System.Console.WriteLine("Concert exception `" + e + "` caught");
}
}
// GED formulation from the paper
// https://ieeexplore.ieee.org/document/1642656
public override void BLPjusticehero()
{
int nbNode1 = graph1.ListNodes.Count;
int nbNode2 = graph2.ListNodes.Count;
int N = nbNode1 + nbNode2; // nombre de noeuds du graphe d'édition
// #region
//création matrices de placement standard A0 et A1
Graph gridg1 = new Graph();
Graph gridg2 = new Graph();
Type typeNodeLabel = graph1.ListNodes[0].Label.GetType();
object objNode = Activator.CreateInstance(typeNodeLabel);
Graphs.Label nodeepslabel = (Graphs.Label)objNode;
nodeepslabel.Id = ConstantsAC.EPS_ID;
Type typeEdgeLabel = null;
object objEdge = null;
Graphs.Label edgeepslabel = null;
if (graph1.ListEdges.Count > 0)
{
typeEdgeLabel = graph1.ListEdges[0].Label.GetType();
objEdge = Activator.CreateInstance(typeEdgeLabel);
edgeepslabel = (Graphs.Label)objEdge;
edgeepslabel.Id = ConstantsAC.EPS_ID;
}
if (graph2.ListEdges.Count > 0)
{
typeEdgeLabel = graph2.ListEdges[0].Label.GetType();
objEdge = Activator.CreateInstance(typeEdgeLabel);
edgeepslabel = (Graphs.Label)objEdge;
edgeepslabel.Id = ConstantsAC.EPS_ID;
}
if (graph1.ListEdges.Count == 0 && graph2.ListEdges.Count == 0)
{
Console.Out.WriteLine("error no edges random edge label alkane");
edgeepslabel = (Graphs.Label) new LabelEdgeAlkane();
edgeepslabel.Id = ConstantsAC.EPS_ID;
}
//else
//{
//edgeepslabel = (Graphs.Label)new LabelEdgeAlkane();
//edgeepslabel.Id = ConstantsAC.EPS_ID;
//}
for (int i = 0; i < nbNode1; i++)
{
gridg1.addNode(graph1.ListNodes[i]);
}
for (int i = 0; i < graph1.ListEdges.Count; i++)
{
gridg1.addEdge(graph1.ListEdges[i]);
}
// ajout des noeuds "virtuels" au graphe g1, pour que g1 corresponde au placement standard dans le graphe d'édition (A0)
for (int i = nbNode1; i < N; i++)
{
Node n = new Node((i + 2).ToString());
gridg1.addNode(n);
n.Label = nodeepslabel;
n.Label.Id = ConstantsAC.EPS_ID;
// LabelEdgeLetter
//n.Label = new Graphs.GenericLabel();
//n.Label.Id = n.Id;
}
MatrixLibrary.Matrix A0 = gridg1.calculateAdjacencyMatrix(); // création matrice d'adajcence de g1
// idem pour g2 (A1)
for (int i = 0; i < nbNode2; i++)
{
gridg2.addNode(graph2.ListNodes[i]);
}
for (int i = 0; i < graph2.ListEdges.Count; i++)
{
gridg2.addEdge(graph2.ListEdges[i]);
}
for (int i = nbNode2; i < N; i++)
{
Node n = new Node((i + 2).ToString());
gridg2.addNode(n);
n.Label = nodeepslabel;//new LabelNodeMutagen();
n.Label.Id = ConstantsAC.EPS_ID;
//n.Label = new Graphs.GenericLabel();
//n.Label.Id = n.Id;
}
MatrixLibrary.Matrix A1 = gridg2.calculateAdjacencyMatrix(); // création matrice d'adajcence de g2
// les graphes vont être étiquetés avec un label LabelNodeMolecule (pour les noeuds) et LabelEdgeMolecule (pour les arrêtes)
// cela va nous permettre d'utiliser notre propre méthode "dissimilarity" pour les noeuds et arrêtes
// gridg1.DynamicCastLabel(graph1.ListNodes[0].Label, graph1.ListEdges[0].Label);
// gridg2.DynamicCastLabel(graph2.ListNodes[0].Label, graph2.ListEdges[0].Label);
// nb variables du pb : matrices P(N*N), S(N*N) et T(N*N)
int nbCols = 3 * (N * N);
// nb contraintes du pb
int nbRows = N * N + N + N;
List <double> objList = new List <double>();
List <string> colNameList = new List <string>();
// coût des opérations d'édition des sommets (coeff de P dans la formule de la distance d'édition)
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
double costNode = gridg1.ListNodes[i].Label.dissimilarity(gridg2.ListNodes[j].Label);
objList.Add(costNode);
//colNameList.Add("P[" + gridg1.ListNodes[i].Id + "][" + gridg2.ListNodes[j].Id + "]");
colNameList.Add("x_" + gridg1.ListNodes[i].Id + "," + gridg2.ListNodes[j].Id + "");
}
}
// coût des opérations d'édition des arrêtes (coeffs de S et T)
//Edge ee = new Edge((0).ToString());
//ee.Label = new LabelEdgeMutagen();
//ee.Label.Id = ConstantsAC.EPS_ID;
// coeff de S
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
// dans notre cas, l'opération est soit 0->1 ou 1->0 (insertion ou suppression d'une arrête)
// double costNode = ee.Label.dissimilarity(ee.Label) / 2.0;
double costNode = edgeepslabel.dissimilarity(edgeepslabel) / 2.0;
//double costNode = 0.5 / 2.0;
objList.Add(costNode);
colNameList.Add("S[" + gridg1.ListNodes[i].Id + "][" + gridg2.ListNodes[j].Id + "]");
}
}
// coeff de T
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
// dans notre cas, l'opération est soit 0->1 ou 1->0 (insertion ou suppression d'une arrête)
//double costNode = ee.Label.dissimilarity(ee.Label) / 2.0;
double costNode = edgeepslabel.dissimilarity(edgeepslabel) / 2.0;
// double costNode = 0.5 / 2.0;
objList.Add(costNode);
colNameList.Add("T[" + gridg1.ListNodes[i].Id + "][" + gridg2.ListNodes[j].Id + "]");
}
}
try
{
// Cplex cplex = new Cplex(); // creation du modèle CPLEX
//ILPMatrix lp_matrix = cplex.AddLPMatrix(); // matrice du pb (initialisée à 0 colonnes et 0 lignes)
cplex = new Cplex();
ilpMatrix = cplex.AddLPMatrix();
ColumnArray colonnes = cplex.ColumnArray(ilpMatrix, nbCols); // définition des variables-colonnes du pb
// ajout des variables-colonnes dans la matrice du pb (avec définition des bornes: P[i][j] = 0 ou 1, idem avec S et T)
INumVar[] x = cplex.NumVarArray(colonnes, 0, 1, NumVarType.Bool, colNameList.ToArray());
INumVar[,] P = new INumVar[N, N];
INumVar[,] S = new INumVar[N, N];
INumVar[,] T = new INumVar[N, N];
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
P[i, j] = x[(N * i) + j];
}
}
// indice de S et T dans x (utilisés lors de la définition des contraintes)
int indicedebutS = N * N; // indice du 1er élément de S dans x
int indicedebutT = 2 * (N * N); // indice du 1er élément de T dans x
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
S[i, j] = x[indicedebutS + (N * i) + j];
}
}
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
T[i, j] = x[indicedebutT + (N * i) + j];
}
}
objCoef = objList.ToArray();
// ajout de la fonction objectif du pb
cplex.AddMinimize(cplex.ScalProd(x, objCoef));
// contrainte n°1
for (int i = 0; i < N; i++)
{
int[] coeffsA0 = new int[N]; // vecteur des coeffs ligne i de A0
INumVar[] coeffsP_A1 = new INumVar[N]; // vecteur des coeffs ligne i de P
for (int c = 0; c < N; c++)
{
coeffsA0[c] = (int)A0[i, c];
coeffsP_A1[c] = P[i, c];
}
for (int j = 0; j < N; j++)
{
INumVar[] coeffsP = new INumVar[N]; // vecteur des coeffs colonne j de P
int[] coeffsA1 = new int[N]; // vecteur des coeffs colonne j de A1
for (int c = 0; c < N; c++)
{
coeffsP[c] = P[c, j];
coeffsA1[c] = (int)A1[c, j];
}
cplex.AddEq(cplex.Sum(
cplex.Diff(
cplex.ScalProd(coeffsP, coeffsA0), cplex.ScalProd(coeffsP_A1, coeffsA1)),
cplex.Diff(
S[i, j], T[i, j]))
, 0);
/* (ANCIEN PRODUIT TERME A TERME)
* cplex.AddEq(cplex.Sum(
* cplex.Diff(
* cplex.Prod(A0[i,j],P[i,j]),cplex.Prod(P[i,j],A1[i,j])),
* cplex.Diff(
* S[i, j], T[i, j]))
* , 0); */
}
}
// contrainte n°2 (somme des lignes dans P = 1 et somme des colonnes dans P = 1)
for (int i = 0; i < N; i++)
{
INumVar[] sommeLignes = new INumVar[N];
INumVar[] sommeColonnes = new INumVar[N];
for (int j = 0; j < N; j++)
{
sommeLignes[j] = x[N * i + j];
sommeColonnes[j] = x[N * j + i];
}
cplex.AddEq(cplex.Sum(sommeLignes), 1);
cplex.AddEq(cplex.Sum(sommeColonnes), 1);
}
}
catch (ILOG.Concert.Exception e)
{
System.Console.WriteLine("Concert exception `" + e + "` caught");
}
}
