Class BidirectionalAStarShortestPath<V,E>

Type Parameters:
V - the graph vertex type
E - the graph edge type
All Implemented Interfaces:
ShortestPathAlgorithm<V,E>

public class BidirectionalAStarShortestPath<V,E> extends BaseBidirectionalShortestPathAlgorithm<V,E>
A bidirectional version of A* algorithm.

See the Wikipedia article for details and references about bidirectional search. This technique does not change the worst-case behavior of the algorithm but reduces, in some cases, the number of visited vertices in practice.

The algorithm was first introduced in Ira Sheldon Pohl. 1969. Bi-Directional and Heuristic Search in Path Problems. Ph.D. Dissertation. Stanford University, Stanford, CA, USA. AAI7001588.

The implementation uses two termination criteria depending on if the provided heuristic is consistent or not. Both criteria are based on the shortest path distance $\mu$ seen thus far in the search. Initially, in both cases the algorithm sets $\mu=\infty$. Whenever the search updates the information about the vertex $v$, it sets $\mu = min\{\mu; g_f(v) + g_b(v)\}$, where $g_f(v)$ is the current best-known path cost from $source$ to $sink$ and $g_b(v)$ is the current best-known path cost from $sink$ to $source$.

See Also:
  • Field Details

    • forwardHeuristic

      private AStarAdmissibleHeuristic<V> forwardHeuristic
      Heuristic used for forward search.
    • backwardHeuristic

      private AStarAdmissibleHeuristic<V> backwardHeuristic
      Heuristic used for backward search. In general $d(u,v)\neq d(v,u)$, e.g. in the directed graphs.
    • heapSupplier

      private final Supplier<org.jheaps.AddressableHeap<Double,V>> heapSupplier
  • Constructor Details

    • BidirectionalAStarShortestPath

      public BidirectionalAStarShortestPath(Graph<V,E> graph, AStarAdmissibleHeuristic<V> heuristic)
      Constructs a new instance of the algorithm for a given graph and heuristic.
      Parameters:
      graph - the graph
      heuristic - heuristic that estimates distances between nodes
    • BidirectionalAStarShortestPath

      public BidirectionalAStarShortestPath(Graph<V,E> graph, AStarAdmissibleHeuristic<V> heuristic, Supplier<org.jheaps.AddressableHeap<Double,V>> heapSupplier)
      Constructs a new instance of the algorithm for a given graph, heuristic and heap supplier.
      Parameters:
      graph - the graph
      heuristic - heuristic that estimates distances between nodes
      heapSupplier - supplier of the preferable heap implementation
  • Method Details

    • getPath

      public GraphPath<V,E> getPath(V source, V sink)
      Get a shortest path from a source vertex to a sink vertex.
      Parameters:
      source - the source vertex
      sink - the target vertex
      Returns:
      a shortest path or null if no path exists