Class AStarShortestPath<V,​E>

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

    public class AStarShortestPath<V,​E>
    extends BaseShortestPathAlgorithm<V,​E>
    A* shortest path.

    An implementation of A* shortest path algorithm. This class works for directed and undirected graphs, as well as multi-graphs and mixed-graphs. The graph can also change between invocations of the getPath(Object, Object) method; no new instance of this class has to be created. The heuristic is implemented using a PairingHeap data structure by default to maintain the set of open nodes. However, there still exist several approaches in literature to improve the performance of this heuristic which one could consider to implement. Custom heap implementation can be specified during the construction time. Another issue to take into consideration is the following: given two candidate nodes, $i$, $j$ to expand, where $f(i)=f(j)$, $g(i)$ > $g(j)$, $h(i)$ < $g(j)$, $f(i)=g(i)+h(i)$, $g(i)$ is the actual distance from the source node to $i$, $h(i)$ is the estimated distance from $i$ to the target node. Usually a depth-first search is desired, so ideally we would expand node $i$ first. Using the PairingHeap, this is not necessarily the case though. This could be improved in a later version.

    Note: This implementation works with both consistent and inconsistent admissible heuristics. For details on consistency, refer to the description of the method AStarAdmissibleHeuristic.isConsistent(Graph). However, this class is not optimized for inconsistent heuristics. Several opportunities to improve both worst case and average runtime complexities for A* with inconsistent heuristics described in literature can be used to improve this implementation!

    • Field Detail

      • heapSupplier

        protected final java.util.function.Supplier<org.jheaps.AddressableHeap<java.lang.Double,​V>> heapSupplier
      • openList

        protected org.jheaps.AddressableHeap<java.lang.Double,​V> openList
      • vertexToHeapNodeMap

        protected java.util.Map<V,​org.jheaps.AddressableHeap.Handle<java.lang.Double,​V>> vertexToHeapNodeMap
      • closedList

        protected java.util.Set<V> closedList
      • gScoreMap

        protected java.util.Map<V,​java.lang.Double> gScoreMap
      • cameFrom

        protected java.util.Map<V,​E> cameFrom
      • numberOfExpandedNodes

        protected int numberOfExpandedNodes
      • comparator

        protected java.util.Comparator<java.lang.Double> comparator
    • Constructor Detail

      • AStarShortestPath

        public AStarShortestPath​(Graph<V,​E> graph,
                                 AStarAdmissibleHeuristic<V> admissibleHeuristic)
        Create a new instance of the A* shortest path algorithm.
        Parameters:
        graph - the input graph
        admissibleHeuristic - admissible heuristic which estimates the distance from a node to the target node. The heuristic must never overestimate the distance.
      • AStarShortestPath

        public AStarShortestPath​(Graph<V,​E> graph,
                                 AStarAdmissibleHeuristic<V> admissibleHeuristic,
                                 java.util.function.Supplier<org.jheaps.AddressableHeap<java.lang.Double,​V>> heapSupplier)
        Create a new instance of the A* shortest path algorithm.
        Parameters:
        graph - the input graph
        admissibleHeuristic - admissible heuristic which estimates the distance from a node to the target node. The heuristic must never overestimate the distance.
        heapSupplier - supplier of the preferable heap implementation
    • Method Detail

      • initialize

        private void initialize​(AStarAdmissibleHeuristic<V> admissibleHeuristic)
        Initializes the data structures.
        Parameters:
        admissibleHeuristic - admissible heuristic
      • getPath

        public GraphPath<V,​E> getPath​(V sourceVertex,
                                            V targetVertex)
        Calculates (and returns) the shortest path from the sourceVertex to the targetVertex. Note: each time you invoke this method, the path gets recomputed.
        Parameters:
        sourceVertex - source vertex
        targetVertex - target vertex
        Returns:
        the shortest path from sourceVertex to targetVertex
      • getNumberOfExpandedNodes

        public int getNumberOfExpandedNodes()
        Returns how many nodes have been expanded in the A* search procedure in its last invocation. A node is expanded if it is removed from the open list.
        Returns:
        number of expanded nodes
      • expandNode

        private void expandNode​(org.jheaps.AddressableHeap.Handle<java.lang.Double,​V> currentNode,
                                V endVertex)
      • buildGraphPath

        private GraphPath<V,​E> buildGraphPath​(V startVertex,
                                                    V targetVertex,
                                                    double pathLength)
        Builds the graph path
        Parameters:
        startVertex - starting vertex of the path
        targetVertex - ending vertex of the path
        pathLength - length of the path
        Returns:
        the shortest path from startVertex to endVertex