标签：ullmann 子图同构算法 ullmann_algorithmiso
子图同构算法Ullmann早在1976年就提出来了，大家有兴趣可以自己去搜索下原文看看。这里我就简要的阐述一下。
给定两个图Q 和 G, 它们相应的矩阵分别是
算法步骤：
Step1. Setup matrix Mn×m , such that M[i][j]=1, if 1) the i-th vertex in Q hasthe same label as the j-th vertex in G; and 2) the i-th vertex has smallervertex degree than the j-th vertex in G.
Step2.MatrixesM are generated by systematically changing to 0 all but one of the 1’s in eachof the rows of M, subject to the definitory condition that no column of amatrix M may contain more than one 1.
Step3.Verify matrix M’ by the following equation
为了提高算法的效率，采用了如下的Refinement。
Refinement:
Letthe i-th vertex v in Q corresponds to the j-th vertex u in G.Each neighbor vertex of v in Q must correspond to some neighbor vertexof u in G. Otherwise, vcannot correspond to u.
1. Considering the matrix M, for each 1 in M, we refine it by the followingequation. If fails, change 1 to 0 in M.
2. If there exists at least one row (in M) having no 1, we report no subgraphisomorphism from Q to G.
接下来就直接粘贴代码了。
package ucas.iie.graph.action;
import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import ucas.iie.graph.bean.EdgeBean;
import ucas.iie.graph.bean.GraphBean;
import ucas.iie.graph.bean.VertexBean;
public class IsomorphismImpl {
private ArrayList<GraphBean> query_g;// 查询的子图
private ArrayList<GraphBean> mydb_g;// 图的总数据
public IsomorphismImpl() {
query_g = new ArrayList<GraphBean>();
mydb_g = new ArrayList<GraphBean>();
}
/**
*
* @param query
* @param db
* @return 返回初始的矩阵M0
*/
public int[][] getMatrixM(GraphBean query, GraphBean db) {
int row = query.getvList().size();
int column = db.getvList().size();
int[][] M0 = new int[row][column];
// System.out.println("M0:");
for (int i = 0; i < row; i++) {
for (int j = 0; j < column; j++) {
String vi = query.getvList().get(i).getVertex();
String vj = db.getvList().get(j).getVertex();
if (db.getVDegree(vj) >= query.getVDegree(vi))
M0[i][j] = 1;
else
M0[i][j] = 0;
// System.out.print(M0[i][j] + " ");
}
// System.out.println("");
}
return M0;
}
public ArrayList<GraphBean> getQuery_g() {
return query_g;
}
public void setQuery_g(ArrayList<GraphBean> query_g) {
this.query_g = query_g;
}
public ArrayList<GraphBean> getMydb_g() {
return mydb_g;
}
public void setMydb_g(ArrayList<GraphBean> mydb_g) {
this.mydb_g = mydb_g;
}
/**
*
* @param queryFile
* 查询子图的路径
* @param dbFile
* 图的总数据路径
* @throws IOException
*/
public void initGraphDB(String queryFile, String dbFile) throws IOException {
// 读取查询子图的数据
BufferedReader q_br = new BufferedReader(new InputStreamReader(
new FileInputStream(queryFile)));
String lineData = q_br.readLine();
GraphBean qgb;
if (lineData.startsWith("t #")) {// 第一个子图
qgb = new GraphBean();
while ((lineData = q_br.readLine()) != null) {
if (lineData.startsWith("t #")) {
this.query_g.add(qgb);
qgb = new GraphBean();
continue;
} else if (lineData.startsWith("v")) { // 顶点
String vs[] = lineData.split(" ");
VertexBean vb = new VertexBean();
vb.setVertex(vs[1]);
vb.setLabel(vs[2]);
qgb.getvList().add(vb);
} else { // 边
String es[] = lineData.split(" ");
EdgeBean eb = new EdgeBean();
eb.setVertex_i(es[1]);
eb.setVertex_j(es[2]);
eb.setLabel_e(es[3]);
qgb.geteList().add(eb);
}
}
}
// 读取图数据
BufferedReader db_br = new BufferedReader(new InputStreamReader(
new FileInputStream(dbFile)));
lineData = db_br.readLine();
GraphBean dbgb;
if (lineData.startsWith("t #")) {//
dbgb = new GraphBean();
while ((lineData = db_br.readLine()) != null) {
if (lineData.startsWith("t #")) {
this.mydb_g.add(dbgb);
dbgb = new GraphBean();
continue;
} else if (lineData.startsWith("v")) { // 顶点
String vs[] = lineData.split(" ");
VertexBean vb = new VertexBean();
vb.setVertex(vs[1]);
vb.setLabel(vs[2]);
dbgb.getvList().add(vb);
} else if (lineData.startsWith("e")) { // 边
String es[] = lineData.split(" ");
EdgeBean eb = new EdgeBean();
eb.setVertex_i(es[1]);
eb.setVertex_j(es[2]);
eb.setLabel_e(es[3]);
dbgb.geteList().add(eb);
}
}
}
}
/**
* 返回边的label
* @param i
* @param j
* @param ebList
* @return
*/
public String getLabel(String i, String j, ArrayList<EdgeBean> ebList) {
for (int k = 0; k < ebList.size(); k++) {
EdgeBean eb = ebList.get(k);
String vi = eb.getVertex_i();
String vj = eb.getVertex_j();
if (i.equals(vi) && j.equals(vj))
return eb.getLabel_e();
else if (j.equals(vi) && i.equals(vj))
return eb.getLabel_e();
}
return null;
}
public boolean isIsomorphism(GraphBean subgraph, GraphBean graphdb) {
int M0[][] = getMatrixM(subgraph, graphdb);
int MA[][] = subgraph.getMatrix();
int MB[][] = graphdb.getMatrix();
ArrayList<EdgeBean> ebq = subgraph.geteList();
ArrayList<EdgeBean> ebdb = graphdb.geteList();
// 对任意的MA[i][x] = 1 ==> 存在y M[x][y]MB[y][j] = 1 否则M0[i][j] = 0
for (int i = 0; i < subgraph.getvList().size(); i++) {
for (int j = 0; j < graphdb.getvList().size(); j++) {
if (M0[i][j] == 1) {
String ilabel = subgraph.getvList().get(i).getLabel();
String jlabel = graphdb.getvList().get(j).getLabel();
if (ilabel.equals(jlabel)) {
for (int x = 0; x < subgraph.getvList().size(); x++) {
boolean tag = false;
if (MA[i][x] == 1) {
String label_ix = getLabel(String.valueOf(i),
String.valueOf(x), ebq);
for (int y = 0; y < graphdb.getvList().size(); y++) {
if (M0[x][y] * MB[y][j] == 1) {
String label_yj = getLabel(
String.valueOf(y),
String.valueOf(j), ebdb);
if (label_ix.equals(label_yj)) {///比较顶点之间的边上的标签，看是否相等。
tag = true;
break;
}
}
}// break
if (!tag) {
M0[i][j] = 0;
break;
}
}
}// break
} else {// if(ilabel.equals(jlabel))
M0[i][j] = 0;
}
}// if (M0[i][j] == 1)
}
}
// System.out.println("M':");
for (int i = 0; i < subgraph.getvList().size(); i++) {
int sumi = 0;
for (int j = 0; j < graphdb.getvList().size(); j++) {
// System.out.print(M0[i][j] + " ");
sumi += M0[i][j];
}
if (sumi == 0) {
// System.out.println("M0有一行元素都是0");
return false;
}// 有一行的元素都是0，直接退出
// System.out.println();
}
int raw = subgraph.getvList().size();
int col = graphdb.getvList().size();
int F[] = new int[col];// F[i] = 1 ,表示第i列已经用过了
int H[] = new int[raw];// H[d] = k ,表示第d行选的是第k列
int d = 0;// M0的第d行
int k = 0;// M0的第k列
int[][][] matrixList = new int[raw][][];// 用来记录每次d所对应的M0
for (int i = 0; i < F.length; i++) {
F[i] = -1;
}
for (int i = 0; i < H.length; i++) {
H[i] = -1;
}
// //////////////////////////////
while (true) {
if (H[d] == -1) {
k = 0;
matrixList[d] = M0;
} else {// 回溯
k = H[d] + 1;
F[H[d]] = -1;
M0 = matrixList[d];
}
while (k < col) {// 也就是M0的列
if (M0[d][k] == 1 && F[k] == -1) {// 这样的列找到后就跳出，其他的在回溯的时候再遍历
break;
}
k++;
}
if (k == col) {// 第d行中没有满足条件的列,回溯到上一层
H[d] = -1;
d--;
} else {// M0[d][k]=1,第d行的其他元素都为0
for (int j = 0; j < col; j++) {
M0[d][j] = 0;
}
M0[d][k] = 1;
H[d] = k;
F[k] = 1;
d++;
}
if (d == -1) {
// System.out.println("不同构");
return false;
}
if (d == raw) {// 即找到了一个M0，接下里就是验证
if (this.isTrueFor(MA, MB, M0)) {// 条件成立
// System.out.println("同构");
return true;
} else {// 回溯
d = raw - 1;
}
}// if
}// while
}
/**
* for all element int MA[i][j]=1 ==> MC=M*{(M*MB)^T},MC[i][j]=1
*
* @param MA
* @param MB
* @param M
* @return
*/
public boolean isTrueFor(int[][] MA, int[][] MB, int M[][]) {
boolean flag = true;
int raw = M.length;
int column = MB[0].length;
int tmp[][] = new int[raw][column];// tmp[][]=M*MB
for (int i = 0; i < raw; i++) {// raws
for (int j = 0; j < column; j++) {// columns
for (int k = 0; k < M[0].length; k++) {
tmp[i][j] += M[i][k] * MB[k][j];
}
}
}
int tmp_t[][] = new int[column][raw];// 转置
for (int i = 0; i < raw; i++) {// raws
for (int j = 0; j < column; j++) {// columns
tmp_t[j][i] = tmp[i][j];
}
}
int MC[][] = new int[MA.length][MA[0].length];
// System.out.println("MC:");
for (int i = 0; i < MA.length; i++) {// raws
for (int j = 0; j < MA[0].length; j++) {// columns
for (int k = 0; k < M[0].length; k++) {
MC[i][j] += M[i][k] * tmp_t[k][j];
}
// System.out.print(MC[i][j] + " ");
}
// System.out.println();
}
for (int i = 0; i < MA.length; i++) {// raws
for (int j = 0; j < MA[0].length; j++) {// columns
if (MA[i][j] == 1) {
if (MC[i][j] == 1)
continue;
else
return false;
}
}
}
return flag;
}
public static void main(String[] args) {
IsomorphismImpl ii = new IsomorphismImpl();
String queryFile = "C:\\Users\\Fernando\\Desktop\\Q24.my";
String dbFile = "C:\\Users\\Fernando\\Desktop\\mygraphdb.data";
try {
ii.initGraphDB(queryFile, dbFile);
ArrayList<GraphBean> query_g = ii.getQuery_g();
System.out.println("子图(size)：" + query_g.size());
ArrayList<GraphBean> db_g = ii.getMydb_g();
System.out.println("总图(size)：" + db_g.size());
for (int i = 0; i < query_g.size(); i++) {
for (int j = 0; j < db_g.size(); j++) {
GraphBean tq = query_g.get(i);
GraphBean tdb = db_g.get(j);
if (ii.isIsomorphism(tq, tdb)) {
System.err.println("t # " + i + " 与 T # " + j + " 同构");
}
}
}
} catch (IOException e) {
// TODO Auto-generated catch block
e.printStackTrace();
}
}
}
package ucas.iie.graph.bean;
import java.util.ArrayList;
public class GraphBean {
/** 图的数据格式
* t # 0 表示第0个图
v 0 2
v 1 2
v 2 2
v 3 2
v 4 2
e 0 1 2
e 1 2 2
e 2 3 2
e 3 4 2
*/
private ArrayList<VertexBean> vList;
private ArrayList<EdgeBean> eList;
public GraphBean(){
vList = new ArrayList<VertexBean>();
eList = new ArrayList<EdgeBean>();
}
public ArrayList<VertexBean> getvList() {
return vList;
}
public void setvList(ArrayList<VertexBean> vList) {
this.vList = vList;
}
public ArrayList<EdgeBean> geteList() {
return eList;
}
public void seteList(ArrayList<EdgeBean> eList) {
this.eList = eList;
}
public int[][] getMatrix(){
int[][] M = new int[vList.size()][vList.size()];
for (int index = 0; index < eList.size(); index++) {
EdgeBean eb = eList.get(index);
int i = Integer.parseInt(eb.getVertex_i());
int j = Integer.parseInt(eb.getVertex_j());
M[i][j] = 1;
M[j][i] = 1;
}
// System.out.println("MA/MB:");
// for (int i = 0; i < vList.size(); i++) {
// for (int j = 0; j < vList.size(); j++) {
// System.out.print(M[i][j] + " ");
// }
// System.out.println();
// }
return M;
}
/**
*
* @param v
* @return 返回顶点v的度
*/
public int getVDegree(String v){
int sumDeg = 0;
for (int i = 0; i < eList.size(); i++) {
if(eList.get(i).getVertex_i().equals(v)||
eList.get(i).getVertex_j().equals(v)){
sumDeg ++;
}
}
return sumDeg;
}
public String toString(){
String res = "";
for (int i = 0; i < this.vList.size(); i++) {
res +="v " + vList.get(i).getVertex() + " " + vList.get(i).getLabel() + "\r\n";
}
for (int j = 0; j < this.eList.size(); j++) {
res +="e " + eList.get(j).getVertex_i() + " " + eList.get(j).getVertex_j() + " "+eList.get(j).getLabel_e() + "\r\n";
}
return res;
}
public static void main(String[] args) {
new GraphBean().getMatrix();
}
}
package ucas.iie.graph.bean;
public class EdgeBean {//“e i j k” 表示图的边<i,j>的label是k
/** 图的数据格式
* t # 0 表示第0个图
v 0 2
v 1 2
v 2 2
v 3 2
v 4 2
e 0 1 2
e 1 2 2
e 2 3 2
e 3 4 2
*/
private String vertex_i;
private String vertex_j;
private String label_e;
public String getVertex_i() {
return vertex_i;
}
public void setVertex_i(String vertex_i) {
this.vertex_i = vertex_i;
}
public String getVertex_j() {
return vertex_j;
}
public void setVertex_j(String vertex_j) {
this.vertex_j = vertex_j;
}
public String getLabel_e() {
return label_e;
}
public void setLabel_e(String label_e) {
this.label_e = label_e;
}
}
package ucas.iie.graph.bean;
public class VertexBean { //“v i j” 表示图的顶点i的label是j
/** 图的数据格式
* t # 0 表示第0个图
v 0 2
v 1 2
v 2 2
v 3 2
v 4 2
e 0 1 2
e 1 2 2
e 2 3 2
e 3 4 2
*/
private String vertex;
private String label;
public String getVertex() {
return vertex;
}
public void setVertex(String vertex) {
this.vertex = vertex;
}
public String getLabel() {
return label;
}
public void setLabel(String label) {
this.label = label;
}
}
子图同构算法Ullmann实现，并采取了Refinement（java语言）
标签：ullmann 子图同构算法 ullmann_algorithmiso
原文地址：http://blog.csdn.net/sh_c1991/article/details/42746429
