有向辺 (u, v) では、u < v を満たすすべての頂点の順序をトポロジカル順序と呼びます。 トポロジカルソートは、有向グラフのトポロジカル順序を計算するために使用されるアルゴリズムです。

具体的なアルゴリズム
  1. グラフから入力辺がない頂点を見つけて出力
  2. グラフから頂点とすべての出力辺を削除
  3. すべての頂点が出力されるまで、上記の手順を繰り返す

サンプルコード

トポロジカル順序付けアルゴリズムのコードは以下のとおりです。
import java.io.IOException;
import org.apache.commons.logging.Log;
import org.apache.commons.logging.LogFactory;
import com.aliyun.odps.data.TableInfo;
import com.aliyun.odps.graph.Aggregator;
import com.aliyun.odps.graph.Combiner;
import com.aliyun.odps.graph.ComputeContext;
Import com. aliyun. ODPS. graph. graphjob;
import com.aliyun.odps.graph.GraphLoader;
import com.aliyun.odps.graph.MutationContext;
import com.aliyun.odps.graph.Vertex;
import com.aliyun.odps.graph.WorkerContext;
import com.aliyun.odps.io.LongWritable;
import com.aliyun.odps.io.NullWritable;
import com.aliyun.odps.io.BooleanWritable;
import com.aliyun.odps.io.WritableRecord;
public class TopologySort {
  private final static Log LOG = LogFactory.getLog(TopologySort.class);
  public static class TopologySortVertex extends
  Vertex<LongWritable, LongWritable, NullWritable, LongWritable> {
    @Override
    public void compute(
    ComputeContext<LongWritable, LongWritable, NullWritable, LongWritable> context,
    Iterable<LongWritable> messages) throws IOException {
      // in superstep 0, each vertex sends message whose value is 1 to its
      // neighbors
      if (context.getSuperstep() == 0) {
        if (hasEdges()) {
          context.sendMessageToNeighbors(this, new LongWritable(1L));
        
      } else if (context.getSuperstep() >= 1) {
        // compute each vertex's indegree
        long indegree = getValue().get();
        for (LongWritable msg : messages) {
          indegree += msg.get();
        
        setValue(new LongWritable(indegree));
        if (indegree == 0) {
          voteToHalt();
          if (hasEdges()) {
            context.sendMessageToNeighbors(this, new LongWritable(-1L));
          
          context.write(new LongWritable(context.getSuperstep()), getId());
          LOG.info("vertex: " + getId());
        
        context.aggregate(new LongWritable(indegree));
      
    
  
  public static class TopologySortVertexReader extends
  GraphLoader<LongWritable, LongWritable, NullWritable, LongWritable> {
    @Override
    public void load(
        LongWritable recordNum,
        WritableRecord record,
        MutationContext<LongWritable, LongWritable, NullWritable, LongWritable> context)
        throws IOException {
      TopologySortVertex vertex = new TopologySortVertex();
      vertex.setId((LongWritable) record.get(0));
      vertex.setValue(new LongWritable(0));
      String[] edges = record.get(1).toString().split(",");
      for (int i = 0; i < edges.length; i++) {
        long edge = Long.parseLong(edges[i]);
        if (edge >= 0) {
          vertex.addEdge(new LongWritable(Long.parseLong(edges[i])),
              NullWritable.get());
        
      
      LOG.info(record.toString());
      context.addVertexRequest(vertex);
    
  
  public static class LongSumCombiner extends
  Combiner<LongWritable, LongWritable> {
    @Override
    public void combine(LongWritable vertexId, LongWritable combinedMessage,
        LongWritable messageToCombine) throws IOException {
      combinedMessage.set(combinedMessage.get() + messageToCombine.get());
    
  
  public static class TopologySortAggregator extends
  Aggregator<BooleanWritable> {
    @SuppressWarnings("rawtypes")
    @Override
    public BooleanWritable createInitialValue(WorkerContext context)
        throws IOException {
      return new BooleanWritable(true);
    
    @Override
    public void aggregate(BooleanWritable value, Object item)
        throws IOException {
      boolean hasCycle = value.get();
      boolean inDegreeNotZero = ((LongWritable) item).get() == 0 ? false : true;
      value.set(hasCycle && inDegreeNotZero);
    
    @Override
    public void merge(BooleanWritable value, BooleanWritable partial)
        throws IOException {
      value.set(value.get() && partial.get());
    
    @SuppressWarnings("rawtypes")
    @Override
    public boolean terminate(WorkerContext context, BooleanWritable value)
        throws IOException {
      if (context.getSuperstep() == 0) {
        // since the initial aggregator value is true, and in superstep we don't
        // do aggregate
        return false;
      
      return value.get();
    
  
  public static void main(String[] args) throws IOException {
    if (args.length ! = 2) {
    System.out.println("Usage : <inputTable> <outputTable>");
      System.exit(-1);
    
    // The input table is in the format of
    // 0 1,2
    // 1 3
    // 2 3
    // 3 -1
    // The first column is vertexid, and the second column is the destination vertexid of the vertex edge. If the value is –1, the vertex does not have any outbound edge
    // The output table is in the format of
    // 0 0
    // 1 1
    // 1 2
    // 2 3
    // The first column is the supstep value, in which the topological sequence is hidden. The second column is vertexid
    // TopologySortAggregator is used to determine if the graph has loops
    // If the input graph has a loop, the iteration ends when the indegree of vertices in the active state is not 0
    // You can use records in the input and output tables to determine if the graph has loops
    GraphJob job = new GraphJob();
    job.setGraphLoaderClass(TopologySortVertexReader.class);
    job.setVertexClass(TopologySortVertex.class);
    job.addInput(TableInfo.builder().tableName(args[0]).build());
    job.addOutput(TableInfo.builder().tableName(args[1]).build());
    job.setCombinerClass(LongSumCombiner.class);
    job.setAggregatorClass(TopologySortAggregator.class);
    long startTime = System.currentTimeMillis();
    job.run();
    System.out.println("Job Finished in "
        + (System.currentTimeMillis() - startTime) / 1000.0 + " seconds");