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

Class 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 BaseManyToManyShortestPaths<V,​E>
    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.

    See Also:
    DefaultManyToManyShortestPaths, DijkstraManyToManyShortestPaths