Class ContractionHierarchyBidirectionalDijkstra<V,E>

Type Parameters:
V - the graph vertex type
E - the graph edge type
All Implemented Interfaces:

public class ContractionHierarchyBidirectionalDijkstra<V,E> extends Object
Implementation of the hierarchical query algorithm based on the bidirectional Dijkstra search. This algorithm is designed to contracted graphs. The best speedup is achieved on sparse graphs with low average outdegree.

The query algorithm is originally described the article: Robert Geisberger, Peter Sanders, Dominik Schultes, and Daniel Delling. 2008. Contraction hierarchies: faster and simpler hierarchical routing in road networks. In Proceedings of the 7th international conference on Experimental algorithms (WEA'08), Catherine C. McGeoch (Ed.). Springer-Verlag, Berlin, Heidelberg, 319-333.

During contraction graph is divided into 2 parts which are called upward and downward graphs. Both parts have all vertices of the original graph. The upward graph ($G_{\uparrow}$) contains only those edges which source has lower level than the target and vice versa for the downward graph ($G_{\downarrow}$).

For the shortest path query from $s$ to $t$, a modified bidirectional Dijkstra shortest path search is performed. The forward search from $s$ operates on $G_{\uparrow}$ and the backward search from $t$ - on the $G_{\downarrow}$. In each direction only the edges of the corresponding part of the graph are considered. Both searches eventually meet at the vertex $v$, which has the highest level in the shortest path from $s$ to $t$. Whenever a search in one direction reaches a vertex that has already been processed in other direction, a new candidate for a shortest path is found. Search is aborted in one direction if the smallest element in the corresponding priority queue is at least as large as the best candidate path found so far.

After computing a contracted path, the algorithm unpacks it recursively into the actual shortest path using the bypassed edges stored in the contraction hierarchy graph.

There is a possibility to provide an already computed contraction for the graph. For now there is no means to ensure that the specified contraction is correct, nor to fail-fast. If algorithm uses an incorrect contraction, the results of the search are unpredictable.

Comparing to usual shortest path algorithm, as DijkstraShortestPath, AStarShortestPath, etc., this algorithm spends time for computing contraction hierarchy but offers significant speedup in shortest path query performance. Therefore it is efficient to use it in order to compute many shortest path on a single graph. Furthermore, on small graphs (i.e with less than 1.000 vertices) the overhead of precomputation is higher than the speed at the stage of computing shortest paths. Typically this algorithm is used to gain speedup for shortest path queries on graphs of middle and large size (i.e. starting at 1.000 vertices). If a further query performance improvement is needed take a look at TransitNodeRoutingShortestPath.

July 2019
Semen Chudakov
See Also:
  • Field Details


      protected static final String GRAPH_CONTAINS_A_NEGATIVE_WEIGHT_CYCLE
      Error message for reporting the existence of a negative-weight cycle.
      See Also:

      protected static final String GRAPH_MUST_CONTAIN_THE_SOURCE_VERTEX
      Error message for reporting that a source vertex is missing.
      See Also:

      protected static final String GRAPH_MUST_CONTAIN_THE_SINK_VERTEX
      Error message for reporting that a sink vertex is missing.
      See Also:
    • graph

      protected final Graph<V,E> graph
      The underlying graph.
  • Constructor Details

  • Method Details

    • getPath

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

      public ShortestPathAlgorithm.SingleSourcePaths<V,E> getPaths(V source)
      Compute all shortest paths starting from a single source vertex.
      Specified by:
      getPaths in interface ShortestPathAlgorithm<V,E>
      source - the source vertex
      the shortest paths
    • getPathWeight

      public double getPathWeight(V source, V sink)
      Get the weight of the shortest path from a source vertex to a sink vertex. Returns Double.POSITIVE_INFINITY if no path exists.
      Specified by:
      getPathWeight in interface ShortestPathAlgorithm<V,E>
      source - the source vertex
      sink - the sink vertex
      the weight of the shortest path from a source vertex to a sink vertex, or Double.POSITIVE_INFINITY if no path exists
    • createEmptyPath

      protected final GraphPath<V,E> createEmptyPath(V source, V sink)
      Create an empty path. Returns null if the source vertex is different than the target vertex.
      source - the source vertex
      sink - the sink vertex
      an empty path or null null if the source vertex is different than the target vertex