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單源最短距離是指給定圖中一個源點，計算源點到其它所有節點的最短距離。Dijkstra算法是求解有向圖中單源最短距離SSSP（Single Source Shortest Path）的經典算法。

算法原理

Dijkstra算法是通過點去更新最短距離值，每個點維護到源點的當前最短距離值，當這個值發生變化時，將新值加上邊的權值，發送消息通知其鄰接點。下一輪迭代時，鄰接點根據收到的消息，更新其當前最短距離值，當所有點的當前最短距離值不再變化時，迭代結束。

初始化：源點s到s自身的距離為0（d[s]=0），其他點u到s的距離為無窮（d[u]=∞）。
迭代：如果存在一條從u到v的邊，則從s到v的最短距離更新為d[v]=min(d[v], d[u]+weight(u, v))，直到所有的點到s的距離不再發生變化時，迭代結束。

說明

對一個有權重的有向圖G=(V,E)，從一個源點s到匯點v有很多路徑，其中邊權和最小的路徑，稱為從s到v的最短距離。

由算法基本原理可以看出，此算法非常適合用MaxCompute Graph程序進行求解。

使用場景

圖類型通常分為有向圖和無向圖兩種，MaxCompute均支持。基于源數據的分布，構造有向圖和無向圖時的路徑通路會存在差異，求解SSSP時會產生不同的結果。MaxCompute Graph以有向圖為基礎數據模型，框架內會以有向圖的模型參與計算。

代碼示例

以下代碼基于不同的場景，提供不同的代碼示例。

有向圖

定義類BaseLoadingVertexResolver，此異常類會在SSSP類中被引用。

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();
  }
}

代碼說明：

第15行：定義BaseLoadingVertexResolver。用于處理有向圖數據在加載過程中所遇到的沖突。
第18行：resolve為處理沖突的具體方法。例如當前的某一頂點進行了兩次添加的過程（即進行了兩次addVertexRequest操作），這種行為便稱為沖突加載，需要人為處理沖突之后再參與計算。

定義類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");
  }
}

代碼說明：

第19行：定義SSSPVertex。其中：
- 點值表示該頂點到源點startVertexId的最短距離。
- compute()方法使用迭代公式d[v]=min(d[v], d[u]+weight(u, v))計算最短距離值并更新至當前點值。
- cleanup()方法將當前頂點到源點的最短距離寫入結果表中。
第54行：當前頂點的Value值（即該頂點到源點的最短路徑）未發生變化時，即調用voteToHalt()通過框架使該頂點進入halt狀態。當所有頂點都進入halt狀態時，計算結束。
第71行：定義GraphLoader圖數據以有向圖的方式加載圖數據。通過將表內存儲的記錄解析為圖的頂點或邊信息加載至框架內。如上示例代碼中，用戶可通過addVertexRequest方式將圖的頂點信息加載至圖計算的上下文內。
第90行：定義MinLongCombiner。對發送給同一個點的消息進行合并，優化性能，減少內存占用。
第101行：主程序main函數中定義GraphJob。指定Vertex、GraphLoader、BaseLoadingVertexResolver、Combiner等的實現，指定輸入輸出表。
第110行：添加處理沖突的類BaseLoadingVertexResolver。

無向圖

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");
    }
}

代碼說明：

第15行：定義SSSPVertex。其中：
- 點值表示該頂點到源點startVertexId的最短距離。
- compute()方法使用迭代公式d[v]=min(d[v], d[u]+weight(u, v))計算最短距離值并更新至當前點值。
- cleanup()方法將當前頂點到源點的最短距離寫入結果表中。
第54行：當前頂點的Value值（即該頂點到源點的最短路徑）未發生變化時，即調用voteToHalt()通過框架使該頂點進入halt狀態。當所有頂點都進入halt狀態時，計算結束。
第61行：定義MinLongCombiner。對發送給同一個點的消息進行合并，優化性能，減少內存占用。
第72行：定義GraphLoader圖數據以無向圖的方式加載圖數據。通過addEdgeRequest以兩點之間的邊作為無向邊加載邊信息，這樣便可保證當前表內存儲的圖信息加載成無向圖。
- 第80行：第一列表示初始點的ID。
- 第81行：第二列表示終點的ID。
- 第82行：第三列表示邊的權重。
- 第83行：創建邊，由終點ID和邊的權重組成。
- 第84行：請求給初始點添加邊。
- 第85行 - 第87行：每條Record表示雙向邊，重復第83行與第84行。
定義SSSPLoadingVertexResolver。用于處理無向圖數據在加載過程中所遇到的沖突。例如當前的某一邊進行了兩次添加的過程（即進行了兩次addEdgeRequest操作），這種行為便稱為沖突加載，需要人為處理重復添加的邊才可保證計算正確性。
第101行：主程序main函數中定義GraphJob。指定Vertex、GraphLoader、SSSPLoadingVertexResolver、Combiner等的實現，指定輸入輸出表。

運行結果

以下是基于有向圖的代碼示例的運行結果。操作詳情，請參見編寫Graph。

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

vertex：代表當前頂點。
value：代表當前vertex到達源點（1）的最短距離。

說明

無向圖數據，用戶可以參考無向圖代碼示例中的初始點ID，終點ID，邊的權值自行構造。

示例教程

關于上述示例代碼的使用詳情，請參見開發Graph。

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算法原理

使用場景

代碼示例

運行結果

示例教程