Module org.jgrapht.core
Package org.jgrapht.alg.shortestpath

Class CHManyToManyShortestPaths<V,E>

java.lang.Object
org.jgrapht.alg.shortestpath.CHManyToManyShortestPaths<V,E>
Type Parameters:
V - the graph vertex type
E - the graph edge type
All Implemented Interfaces:
ManyToManyShortestPathsAlgorithm<V,E>, ShortestPathAlgorithm<V,E>
public class CHManyToManyShortestPaths<V,E> extends Object
Efficient algorithm for the many-to-many shortest paths problem based on contraction hierarchy.

The algorithm is originally described in the article: Sebastian Knopp, Peter Sanders, Dominik Schultes, Frank Schulz, and Dorothea Wagner. 2007. Computing many-to-many shortest paths using highway hierarchies. In Proceedings of the Meeting on Algorithm Engineering & Expermiments. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 36-45.

First contraction hierarchy is constructed. Then for each target vertex a backward single source shortest paths search is performed on the contracted graph. During the searches a bucket $b(v)$ is associated with each vertex $v$ in the graph. A bucket stores a set of pairs $(t,d)$, where $t$ is a target vertex current search is performed from and $d$ is the computed distance from $v$ to this target. Then a forward single source shortest paths search is performed from every source vertex. When a search settles a vertex $v$ with distance $d(s,v)$, where $s$ is current source vertex, its bucket is scanned. For each entry $(t,d)$ if $d(s,t) > d(s,v) + d$ values of paths weight between $s$ and $t$ and its middle vertex is updated. The middle vertices are then used to restored actual path from the information in the shortest paths trees.

Additionally if $|S| > |T|$ the algorithm is executed on the reversed graph. This allows to reduce the number of buckets and optimize memory usage of the algorithm.

The efficiency of this algorithm is derived from the fact that contraction hierarchy produces fairly small shortest paths trees. This allows to both speedup the computations and decrease memory usage to store the paths. The bottleneck of the algorithm is the contraction hierarchy computation, which can lead to significant overhead for dense graphs both in terms of running time and space complexity. Therefore the ideal use cases for this algorithm are sparse graphs of any size with low average out-degree of vertices.

Author:
Semen Chudakov
See Also:

  • Field Details

    • graph

      protected final Graph<V,E> graph

  • Constructor Details

    • CHManyToManyShortestPaths

      public CHManyToManyShortestPaths(Graph<V,E> graph, ThreadPoolExecutor executor)
      Constructs an instance of the algorithm for a given graph and executor. It is up to a user of this algorithm to handle the creation and termination of the provided executor. For utility methods to manage a ThreadPoolExecutor see ConcurrencyUtil.
      Parameters:
      graph - a graph
      executor - executor which will be used to compute ContractionHierarchyPrecomputation.ContractionHierarchy

    • CHManyToManyShortestPaths

      public CHManyToManyShortestPaths(ContractionHierarchyPrecomputation.ContractionHierarchy<V,E> contractionHierarchy)
      Constructs an instance of the algorithm for a given contractionHierarchy.
      Parameters:
      contractionHierarchy - contraction of the graph

  • Method Details

    • getManyToManyPaths

      public ManyToManyShortestPathsAlgorithm.ManyToManyShortestPaths<V,E> getManyToManyPaths(Set<V> sources, Set<V> targets)
      Computes shortest paths from all vertices in sources to all vertices in targets.
      Parameters:
      sources - list of sources vertices
      targets - list of target vertices
      Returns:
      computed shortest paths

    • getPath

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

    • 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>
      Parameters:
      source - the source vertex
      sink - the sink vertex
      Returns:
      the weight of the shortest path from a source vertex to a sink vertex, or Double.POSITIVE_INFINITY 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>
      Parameters:
      source - the source vertex
      Returns:
      the shortest paths

    • getShortestPathsTree

      protected static <V, E> ShortestPathAlgorithm.SingleSourcePaths<V,E> getShortestPathsTree(Graph<V,E> graph, V source, Set<V> targets)
      Computes shortest paths tree starting at source and stopping as soon as all of the targets are reached. Here the DijkstraClosestFirstIterator is used.
      Type Parameters:
      V - the graph vertex type
      E - the graph edge type
      Parameters:
      graph - a graph
      source - source vertex
      targets - target vertices
      Returns:
      shortest paths starting from source and reaching all targets