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首页 云原生大数据计算服务 MaxCompute 操作指南 开发参考：多引擎 Graph 示例程序 单源最短距离

单源最短距离

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单源最短距离是指给定图中一个源点，计算源点到其它所有节点的最短距离。Dijkstra算法是求解有向图中单源最短距离SSSP（Single Source Shortest Path）的经典算法。

算法原理

Dijkstra算法是通过点去更新最短距离值，每个点维护到源点的当前最短距离值，当这个值发生变化时，将新值加上边的权值，发送消息通知其邻接点。下一轮迭代时，邻接点根据收到的消息，更新其当前最短距离值，当所有点的当前最短距离值不再变化时，迭代结束。

  • 初始化：源点s到s自身的距离为0（d[s]=0），其他点u到s的距离为无穷（d[u]=∞）。

  • 迭代：如果存在一条从u到v的边，则从s到v的最短距离更新为d[v]=min(d[v], d[u]+weight(u, v))，直到所有的点到s的距离不再发生变化时，迭代结束。

说明

对一个有权重的有向图G=(V,E)，从一个源点s到汇点v有很多路径，其中边权和最小的路径，称为从s到v的最短距离。

由算法基本原理可以看出，此算法非常适合用MaxCompute Graph程序进行求解。

使用场景

图类型通常分为有向图和无向图两种，MaxCompute均支持。基于源数据的分布，构造有向图和无向图时的路径通路会存在差异，求解SSSP时会产生不同的结果。MaxCompute Graph以有向图为基础数据模型，框架内会以有向图的模型参与计算。

代码示例

以下代码基于不同的场景，提供不同的代码示例。

  • 有向图

    • 定义类BaseLoadingVertexResolver，此异常类会在SSSP类中被引用。

      import com.aliyun.odps.graph.Edge;
import com.aliyun.odps.graph.LoadingVertexResolver;
import com.aliyun.odps.graph.Vertex;
import com.aliyun.odps.graph.VertexChanges;
import com.aliyun.odps.io.Writable;
import com.aliyun.odps.io.WritableComparable;

import java.io.IOException;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Set;

@SuppressWarnings("rawtypes")
public class BaseLoadingVertexResolver<I extends WritableComparable, V extends Writable, E extends Writable, M extends Writable>
        extends LoadingVertexResolver<I, V, E, M> {
  @Override
  public Vertex<I, V, E, M> resolve(I vertexId, VertexChanges<I, V, E, M> vertexChanges) throws IOException {

    Vertex<I, V, E, M> vertex = addVertexIfDesired(vertexId, vertexChanges);

    if (vertex != null) {
      addEdges(vertex, vertexChanges);
    } else {
      System.err.println("Ignore all addEdgeRequests for vertex#" + vertexId);
    }
    return vertex;
  }

  protected Vertex<I, V, E, M> addVertexIfDesired(
          I vertexId,
          VertexChanges<I, V, E, M> vertexChanges) {
    Vertex<I, V, E, M> vertex = null;
    if (hasVertexAdditions(vertexChanges)) {
      vertex = vertexChanges.getAddedVertexList().get(0);
    }

    return vertex;
  }

  protected void addEdges(Vertex<I, V, E, M> vertex,
                          VertexChanges<I, V, E, M> vertexChanges) throws IOException {
    Set<I> destVertexId = new HashSet<I>();
    if (vertex.hasEdges()) {
      List<Edge<I, E>> edgeList = vertex.getEdges();
      for (Iterator<Edge<I, E>> edges = edgeList.iterator(); edges.hasNext(); ) {
        Edge<I, E> edge = edges.next();
        if (destVertexId.contains(edge.getDestVertexId())) {
          edges.remove();
        } else {
          destVertexId.add(edge.getDestVertexId());
        }
      }
    }

    for (Vertex<I, V, E, M> vertex1 : vertexChanges.getAddedVertexList()) {
      if (vertex1.hasEdges()) {
        List<Edge<I, E>> edgeList = vertex1.getEdges();
        for (Edge<I, E> edge : edgeList) {
          if (destVertexId.contains(edge.getDestVertexId())) continue;
          destVertexId.add(edge.getDestVertexId());
          vertex.addEdge(edge.getDestVertexId(), edge.getValue());
        }
      }
    }
  }

  protected boolean hasVertexAdditions(VertexChanges<I, V, E, M> changes) {
    return changes != null && changes.getAddedVertexList() != null
            && !changes.getAddedVertexList().isEmpty();
  }
}

      代码说明：

      • 第15行：定义BaseLoadingVertexResolver。用于处理有向图数据在加载过程中所遇到的冲突。

      • 第18行：resolve为处理冲突的具体方法。例如当前的某一顶点进行了两次添加的过程（即进行了两次addVertexRequest操作），这种行为便称为冲突加载，需要人为处理冲突之后再参与计算。

    • 定义类SSSP。

      import java.io.IOException;

import com.aliyun.odps.graph.Combiner;
import com.aliyun.odps.graph.ComputeContext;
import com.aliyun.odps.graph.Edge;
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.WritableRecord;
import com.aliyun.odps.io.LongWritable;
import com.aliyun.odps.data.TableInfo;

public class SSSP {
  public static final String START_VERTEX = "sssp.start.vertex.id";

  public static class SSSPVertex extends
          Vertex<LongWritable, LongWritable, LongWritable, LongWritable> {
    private static long startVertexId = -1;

    public SSSPVertex() {
      this.setValue(new LongWritable(Long.MAX_VALUE));
    }

    public boolean isStartVertex(
            ComputeContext<LongWritable, LongWritable, LongWritable, LongWritable> context) {
      if (startVertexId == -1) {
        String s = context.getConfiguration().get(START_VERTEX);
        startVertexId = Long.parseLong(s);
      }
      return getId().get() == startVertexId;
    }

    @Override
    public void compute(
            ComputeContext<LongWritable, LongWritable, LongWritable, LongWritable> context,
            Iterable<LongWritable> messages) throws IOException {
      long minDist = isStartVertex(context) ? 0 : Long.MAX_VALUE;
      for (LongWritable msg : messages) {
        if (msg.get() < minDist) {
          minDist = msg.get();
        }
      }
      if (minDist < this.getValue().get()) {
        this.setValue(new LongWritable(minDist));
        if (hasEdges()) {
          for (Edge<LongWritable, LongWritable> e : this.getEdges()) {
            context.sendMessage(e.getDestVertexId(), new LongWritable(minDist + e.getValue().get()));
          }
        }
      } else {
        voteToHalt();
      }
    }

    @Override
    public void cleanup(
            WorkerContext<LongWritable, LongWritable, LongWritable, LongWritable> context)
            throws IOException {
      context.write(getId(), getValue());
    }

    @Override
    public String toString() {
      return "Vertex(id=" + this.getId() + ",value=" + this.getValue() + ",#edges=" + this.getEdges() + ")";
    }
  }

  public static class SSSPGraphLoader extends
          GraphLoader<LongWritable, LongWritable, LongWritable, LongWritable> {
    @Override
    public void load(
            LongWritable recordNum,
            WritableRecord record,
            MutationContext<LongWritable, LongWritable, LongWritable, LongWritable> context)
            throws IOException {
      SSSPVertex vertex = new SSSPVertex();
      vertex.setId((LongWritable) record.get(0));
      String[] edges = record.get(1).toString().split(",");
      for (String edge : edges) {
        String[] ss = edge.split(":");
        vertex.addEdge(new LongWritable(Long.parseLong(ss[0])), new LongWritable(Long.parseLong(ss[1])));
      }
      context.addVertexRequest(vertex);
    }
  }

  public static class MinLongCombiner extends
          Combiner<LongWritable, LongWritable> {
    @Override
    public void combine(LongWritable vertexId, LongWritable combinedMessage,
                        LongWritable messageToCombine) throws IOException {
      if (combinedMessage.get() > messageToCombine.get()) {
        combinedMessage.set(messageToCombine.get());
      }
    }
  }

  public static void main(String[] args) throws IOException {
    if (args.length < 3) {
      System.out.println("Usage: <startnode> <input> <output>");
      System.exit(-1);
    }
    GraphJob job = new GraphJob();
    job.setGraphLoaderClass(SSSPGraphLoader.class);
    job.setVertexClass(SSSPVertex.class);
    job.setCombinerClass(MinLongCombiner.class);
    job.setLoadingVertexResolver(BaseLoadingVertexResolver.class);
    job.set(START_VERTEX, args[0]);
    job.addInput(TableInfo.builder().tableName(args[1]).build());
    job.addOutput(TableInfo.builder().tableName(args[2]).build());
    long startTime = System.currentTimeMillis();
    job.run();
    System.out.println("Job Finished in "
            + (System.currentTimeMillis() - startTime) / 1000.0 + " seconds");
  }
}

      代码说明：

      • 第19行：定义SSSPVertex。其中：

        • 点值表示该顶点到源点startVertexId的最短距离。

        • compute()方法使用迭代公式d[v]=min(d[v], d[u]+weight(u, v))计算最短距离值并更新至当前点值。

        • cleanup()方法将当前顶点到源点的最短距离写入结果表中。

      • 第54行：当前顶点的Value值（即该顶点到源点的最短路径）未发生变化时，即调用voteToHalt()通过框架使该顶点进入halt状态。当所有顶点都进入halt状态时，计算结束。

      • 第71行：定义GraphLoader图数据以有向图的方式加载图数据。通过将表内存储的记录解析为图的顶点或边信息加载至框架内。如上示例代码中，用户可通过addVertexRequest方式将图的顶点信息加载至图计算的上下文内。

      • 第90行：定义MinLongCombiner。对发送给同一个点的消息进行合并，优化性能，减少内存占用。

      • 第101行：主程序main函数中定义GraphJob。指定Vertex、GraphLoader、BaseLoadingVertexResolver、Combiner等的实现，指定输入输出表。

      • 第110行：添加处理冲突的类BaseLoadingVertexResolver。

  • 无向图

    import com.aliyun.odps.data.TableInfo;
import com.aliyun.odps.graph.*;
import com.aliyun.odps.io.DoubleWritable;
import com.aliyun.odps.io.LongWritable;
import com.aliyun.odps.io.WritableRecord;

import java.io.IOException;
import java.util.HashSet;
import java.util.Set;

public class SSSPBenchmark4 {
    public static final String START_VERTEX = "sssp.start.vertex.id";

    public static class SSSPVertex extends
            Vertex<LongWritable, DoubleWritable, DoubleWritable, DoubleWritable> {
        private static long startVertexId = -1;
        public SSSPVertex() {
            this.setValue(new DoubleWritable(Double.MAX_VALUE));
        }
        public boolean isStartVertex(
                ComputeContext<LongWritable, DoubleWritable, DoubleWritable, DoubleWritable> context) {
            if (startVertexId == -1) {
                String s = context.getConfiguration().get(START_VERTEX);
                startVertexId = Long.parseLong(s);
            }
            return getId().get() == startVertexId;
        }

        @Override
        public void compute(
                ComputeContext<LongWritable, DoubleWritable, DoubleWritable, DoubleWritable> context,
                Iterable<DoubleWritable> messages) throws IOException {
            double minDist = isStartVertex(context) ? 0 : Double.MAX_VALUE;
            for (DoubleWritable msg : messages) {
                if (msg.get() < minDist) {
                    minDist = msg.get();
                }
            }
            if (minDist < this.getValue().get()) {
                this.setValue(new DoubleWritable(minDist));
                if (hasEdges()) {
                    for (Edge<LongWritable, DoubleWritable> e : this.getEdges()) {
                        context.sendMessage(e.getDestVertexId(), new DoubleWritable(minDist
                                + e.getValue().get()));
                    }
                }
            } else {
                voteToHalt();
            }
        }

        @Override
        public void cleanup(
                WorkerContext<LongWritable, DoubleWritable, DoubleWritable, DoubleWritable> context)
                throws IOException {
            context.write(getId(), getValue());
        }
    }

    public static class MinLongCombiner extends
            Combiner<LongWritable, DoubleWritable> {
        @Override
        public void combine(LongWritable vertexId, DoubleWritable combinedMessage,
                            DoubleWritable messageToCombine) {
            if (combinedMessage.get() > messageToCombine.get()) {
                combinedMessage.set(messageToCombine.get());
            }
        }
    }

    public static class SSSPGraphLoader extends
            GraphLoader<LongWritable, DoubleWritable, DoubleWritable, DoubleWritable> {
        @Override
        public void load(
                LongWritable recordNum,
                WritableRecord record,
                MutationContext<LongWritable, DoubleWritable, DoubleWritable, DoubleWritable> context)
                throws IOException {
            LongWritable sourceVertexID = (LongWritable) record.get(0);
            LongWritable destinationVertexID = (LongWritable) record.get(1);
            DoubleWritable edgeValue = (DoubleWritable) record.get(2);
            Edge<LongWritable, DoubleWritable> edge = new Edge<LongWritable, DoubleWritable>(destinationVertexID, edgeValue);
            context.addEdgeRequest(sourceVertexID, edge);
            Edge<LongWritable, DoubleWritable> edge2 = new
                    Edge<LongWritable, DoubleWritable>(sourceVertexID, edgeValue);
            context.addEdgeRequest(destinationVertexID, edge2);
        }
    }

    public static class SSSPLoadingVertexResolver extends
            LoadingVertexResolver<LongWritable, DoubleWritable, DoubleWritable, DoubleWritable> {

        @Override
        public Vertex<LongWritable, DoubleWritable, DoubleWritable, DoubleWritable> resolve(
                LongWritable vertexId,
                VertexChanges<LongWritable, DoubleWritable, DoubleWritable, DoubleWritable> vertexChanges) throws IOException {

            SSSPVertex computeVertex = new SSSPVertex();
            computeVertex.setId(vertexId);
            Set<LongWritable> destinationVertexIDSet = new HashSet<>();

            if (hasEdgeAdditions(vertexChanges)) {
                for (Edge<LongWritable, DoubleWritable> edge : vertexChanges.getAddedEdgeList()) {
                    if (!destinationVertexIDSet.contains(edge.getDestVertexId())) {
                        destinationVertexIDSet.add(edge.getDestVertexId());
                        computeVertex.addEdge(edge.getDestVertexId(), edge.getValue());
                    }

                }
            }

            return computeVertex;
        }

        protected boolean hasEdgeAdditions(VertexChanges<LongWritable, DoubleWritable, DoubleWritable, DoubleWritable> changes) {
            return changes != null && changes.getAddedEdgeList() != null
                    && !changes.getAddedEdgeList().isEmpty();
        }
    }

    public static void main(String[] args) throws IOException {
        if (args.length < 2) {
            System.out.println("Usage: <startnode> <input> <output>");
            System.exit(-1);
        }
        GraphJob job = new GraphJob();
        job.setGraphLoaderClass(SSSPGraphLoader.class);
        job.setLoadingVertexResolver(SSSPLoadingVertexResolver.class);
        job.setVertexClass(SSSPVertex.class);
        job.setCombinerClass(MinLongCombiner.class);
        job.set(START_VERTEX, args[0]);
        job.addInput(TableInfo.builder().tableName(args[1]).build());
        job.addOutput(TableInfo.builder().tableName(args[2]).build());
        long startTime = System.currentTimeMillis();
        job.run();
        System.out.println("Job Finished in "
                + (System.currentTimeMillis() - startTime) / 1000.0 + " seconds");
    }
}

    代码说明：

    • 第15行：定义SSSPVertex。其中：

      • 点值表示该顶点到源点startVertexId的最短距离。

      • compute()方法使用迭代公式d[v]=min(d[v], d[u]+weight(u, v))计算最短距离值并更新至当前点值。

      • cleanup()方法将当前顶点到源点的最短距离写入结果表中。

    • 第54行：当前顶点的Value值（即该顶点到源点的最短路径）未发生变化时，即调用voteToHalt()通过框架使该顶点进入halt状态。当所有顶点都进入halt状态时，计算结束。

    • 第61行：定义MinLongCombiner。对发送给同一个点的消息进行合并，优化性能，减少内存占用。

    • 第72行：定义GraphLoader图数据以无向图的方式加载图数据。通过addEdgeRequest以两点之间的边作为无向边加载边信息，这样便可保证当前表内存储的图信息加载成无向图。

      • 第80行：第一列表示初始点的ID。

      • 第81行：第二列表示终点的ID。

      • 第82行：第三列表示边的权重。

      • 第83行：创建边，由终点ID和边的权重组成。

      • 第84行：请求给初始点添加边。

      • 第85行 - 第87行：每条Record表示双向边，重复第83行与第84行。

    • 定义SSSPLoadingVertexResolver。用于处理无向图数据在加载过程中所遇到的冲突。例如当前的某一边进行了两次添加的过程（即进行了两次addEdgeRequest操作），这种行为便称为冲突加载，需要人为处理重复添加的边才可保证计算正确性。

    • 第101行：主程序main函数中定义GraphJob。指定Vertex、GraphLoader、SSSPLoadingVertexResolver、Combiner等的实现，指定输入输出表。

运行结果

以下是基于有向图的代码示例的运行结果。操作详情，请参见编写Graph。

vertex    value
1        0
2        2
3        1
4        3
5        2

  • vertex：代表当前顶点。

  • value：代表当前vertex到达源点（1）的最短距离。

说明

无向图数据，用户可以参考无向图代码示例中的初始点ID，终点ID，边的权值自行构造。

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