Class HeavyPathDecomposition<V,​E>

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

    public class HeavyPathDecomposition<V,​E>
    extends java.lang.Object
    implements TreeToPathDecompositionAlgorithm<V,​E>
    Algorithm for computing the heavy path decomposition of a rooted tree/forest.

    Heavy path decomposition is a technique for decomposing a rooted tree/forest into a set of disjoint paths.

    The techniques was first introduced in Sleator, D. D.; Tarjan, R. E. (1983). "A Data Structure for Dynamic Trees". Proceedings of the thirteenth annual ACM symposium on Theory of computing - STOC '81 doi:10.1145/800076.802464

    In a heavy path decomposition, the edges set is partitioned into two sets, a set of heavy edges and a set of light ones according to the relative number of nodes in the vertex's subtree. We define the size of a vertex v in the forest, denoted by size(v), to be the number of descendants of v, including v itself. We define a tree edge (v,parent(v)) to be heavy if $2*size(v)$ > $size(parent(v))$ and light, otherwise. The set of heavy edges form the edges of the decomposition.

    A benefit of this decomposition is that on any root-to-leaf path of a tree with n nodes, there can be at most $log_2(n)$ light edges.

    This implementation runs in $O(|V|)$ time and requires $O(|V|)$ extra memory, where $|V|$ is the number of vertices in the tree/forest.

    Note: If an edge is not reachable from any of the roots provided, then that edge is neither light nor heavy.

    Alexandru Valeanu
    • Constructor Detail

      • HeavyPathDecomposition

        public HeavyPathDecomposition​(Graph<V,​E> tree,
                                      V root)
        Create an instance with a reference to the tree that we will decompose and to the root of the tree. Note: The constructor will NOT check if the input graph is a valid tree.
        tree - the input tree
        root - the root of the tree
      • HeavyPathDecomposition

        public HeavyPathDecomposition​(Graph<V,​E> forest,
                                      java.util.Set<V> roots)
        Create an instance with a reference to the forest that we will decompose and to the sets of roots of the forest (one root per tree). Note: If two roots appear in the same tree, an error will be thrown. Note: The constructor will NOT check if the input graph is a valid forest.
        forest - the input forest
        roots - the set of roots of the graph
    • Method Detail

      • getHeavyEdges

        public java.util.Set<E> getHeavyEdges()
        Set of heavy edges.
        (immutable) set of heavy edges
      • getLightEdges

        public java.util.Set<E> getLightEdges()
        Set of light edges.
        (immutable) set of light edges
      • getInternalState

        public HeavyPathDecomposition.InternalState getInternalState()
        Return the internal representation of the data. Note: this data representation is intended only for use by other components within JGraphT
        the internal state representation