Package org.graphstream.algorithm

Class AStar

java.lang.Object
org.graphstream.algorithm.AStar
All Implemented Interfaces:
Algorithm
public class AStar
extends Object
implements Algorithm
An implementation of the A* algorithm.

A* computes the shortest path from a node to another in a graph. It guarantees that the path found is the shortest one, given its heuristic is admissible, and a path exists between the two nodes. It will fail if the two nodes are in two distinct connected components.

In this A* implementation, the various costs (often called g, h and f) are given by a AStar.Costs class. This class must provide a way to compute:

  • The cost of moving from a node to another, often called g;
  • The estimated cost from a node to the destination, the heuristic, often noted h;
  • f is the sum of g and h and is computed automatically.

By default the AStar.Costs implementation used uses a heuristic that always returns 0. This makes A* an * equivalent of the Dijkstra algorithm, but also makes it less efficient.

If there are several equivalent shortest paths between the two nodes, the returned one is arbitrary. Therefore this AStar algorithm works with multi-graphs but if two edges between two nodes have the same properties, the one that will be chosen will be arbitrary.

Usage

The basic usage is to create an instance of A* (optionally specify a AStar.Costs object), then to ask it to compute from a shortest path from one target to one destination, and finally to ask for that path: 

 AStart astar = new AStar(graph); 
 astar.compute("A", "Z"); // with A and Z node identifiers in the graph. 
 Path path = astar.getShortestPath();

The advantage of A* is that it can consider any cost function to drive the search. You can (and should) create your own cost functions implementing the AStar.Costs interface.

You can also test the default euclidean "distance" cost function on a graph that has "x" and "y" values. You specify the AStar.Costs function before calling the compute(String,String) method: 

 AStart astar = new AStar(graph); 
 astar.setCosts(new DistanceCosts());
 astar.compute("A", "Z"); 
 Path path = astar.getShortestPath();

Example

 import java.io.IOException;
 import java.io.StringReader;
 
 import org.graphstream.algorithm.AStar;
 import org.graphstream.algorithm.AStar.DistanceCosts;
 import org.graphstream.graph.Graph;
 import org.graphstream.graph.implementations.DefaultGraph;
 import org.graphstream.stream.file.FileSourceDGS;
 
 public class AStarTest {
        
        //     B-(1)-C
        //    /       \
        //  (1)       (10)
        //  /           \
        // A             F
        //  \           /
        //  (1)       (1)
        //    \       /
        //     D-(1)-E
        static String my_graph = 
                "DGS004\n" 
                + "my 0 0\n" 
                + "an A xy: 0,1\n" 
                + "an B xy: 1,2\n"
                + "an C xy: 2,2\n"
                + "an D xy: 1,0\n"
                + "an E xy: 2,0\n"
                + "an F xy: 3,1\n"
                + "ae AB A B weight:1 \n"
                + "ae AD A D weight:1 \n"
                + "ae BC B C weight:1 \n"
                + "ae CF C F weight:10 \n"
                + "ae DE D E weight:1 \n"
                + "ae EF E F weight:1 \n"
                ;
 
        public static void main(String[] args) throws IOException {
                Graph graph = new DefaultGraph("A* Test");
                StringReader reader = new StringReader(my_graph);
 
                FileSourceDGS source = new FileSourceDGS();
                source.addSink(graph);
                source.readAll(reader);
 
                AStar astar = new AStar(graph);
                //astar.setCosts(new DistanceCosts());
                astar.compute("C", "F");
 
                System.out.println(astar.getShortestPath());
        }
 }
Computational Complexity :
The complexity of A* depends on the heuristic.

  • Nested Class Summary

    Nested Classes 
    Modifier and Type Class Description
    static interface  AStar.Costs
    the distance between the current position and the target.
    static class  AStar.DefaultCosts
    An implementation of the Costs interface that provides a default heuristic.
    static class  AStar.DistanceCosts
    An implementation of the Costs interface that assume that the weight of edges is an Euclidean distance in 2D or 3D.

  • Constructor Summary

    Constructors 
    Constructor Description
    AStar()
    New A* algorithm.
    AStar​(org.graphstream.graph.Graph graph)
    New A* algorithm on a given graph.
    AStar​(org.graphstream.graph.Graph graph, String src, String trg)
    New A* algorithm on the given graph.

  • Method Summary

    Modifier and Type Method Description
    org.graphstream.graph.Path buildPath​(org.graphstream.algorithm.AStar.AStarNode target)
    Build the shortest path from the target/destination node, following the parent links.
    void compute()
    Run the algorithm.
    void compute​(String source, String target)
    Call compute() after having called setSource(String) and setTarget(String).
    org.graphstream.graph.Path getShortestPath()
    The computed path, or null if nor result was found.
    void init​(org.graphstream.graph.Graph graph)
    Initialization of the algorithm.
    boolean noPathFound()
    After having called compute() or compute(String, String), if the getShortestPath() returns null, or this method return true, there is no path from the given source node to the given target node.
    void setCosts​(AStar.Costs costs)
    Specify how various costs are computed.
    void setSource​(String nodeName)
    Change the source node.
    void setTarget​(String nodeName)
    Change the target node.

    Methods inherited from class java.lang.Object

    equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • AStar

      public AStar()
      New A* algorithm.

    • AStar

      public AStar​(org.graphstream.graph.Graph graph)
      New A* algorithm on a given graph.
      Parameters:
      graph - The graph where the algorithm will compute paths.

    • AStar

      public AStar​(org.graphstream.graph.Graph graph, String src, String trg)
      New A* algorithm on the given graph.
      Parameters:
      graph - The graph where the algorithm will compute paths.
      src - The start node.
      trg - The destination node.

  • Method Details

    • setSource

      public void setSource​(String nodeName)
      Change the source node. This clears the already computed path, but preserves the target node name.
      Parameters:
      nodeName - Identifier of the source node.

    • setTarget

      public void setTarget​(String nodeName)
      Change the target node. This clears the already computed path, but preserves the source node name.
      Parameters:
      nodeName - Identifier of the target node.

    • setCosts

      public void setCosts​(AStar.Costs costs)
      Specify how various costs are computed. The costs object is in charge of computing the cost of displacement from one node to another (and therefore allows to compute the cost from the source node to any node). It also allows to compute the heuristic to use for evaluating the cost from the current position to the target node. Calling this DOES NOT clear the currently computed paths.
      Parameters:
      costs - The cost method to use.

    • init

      public void init​(org.graphstream.graph.Graph graph)
      Description copied from interface: Algorithm
      Initialization of the algorithm. This method has to be called before the Algorithm.compute() method to initialize or reset the algorithm according to the new given graph.
      Specified by:
      init in interface Algorithm
      Parameters:
      graph - The graph this algorithm is using.

    • compute

      public void compute()
      Description copied from interface: Algorithm
      Run the algorithm. The Algorithm.init(Graph) method has to be called before computing.
      Specified by:
      compute in interface Algorithm
      See Also:
      Algorithm.init(Graph)

    • getShortestPath

      public org.graphstream.graph.Path getShortestPath()
      The computed path, or null if nor result was found.
      Returns:
      The computed path, or null if no path was found.

    • noPathFound

      public boolean noPathFound()
      After having called compute() or compute(String, String), if the getShortestPath() returns null, or this method return true, there is no path from the given source node to the given target node. In other words, the graph has several connected components. It also return true if the algorithm did not run.
      Returns:
      True if there is no possible path from the source to the destination or if the algorithm did not run.

    • buildPath

      public org.graphstream.graph.Path buildPath​(org.graphstream.algorithm.AStar.AStarNode target)
      Build the shortest path from the target/destination node, following the parent links.
      Parameters:
      target - The destination node.
      Returns:
      The path.

    • compute

      public void compute​(String source, String target)
      Call compute() after having called setSource(String) and setTarget(String).
      Parameters:
      source - Identifier of the source node.
      target - Identifier of the target node.