Module org.jgrapht.core
Package org.jgrapht.alg.decomposition

Class HeavyPathDecomposition<V,E>

java.lang.Object
org.jgrapht.alg.decomposition.HeavyPathDecomposition<V,E>
Type Parameters:
V - the graph vertex type
E - the graph edge type
All Implemented Interfaces:
TreeToPathDecompositionAlgorithm<V,E>
public class HeavyPathDecomposition<V,E> extends 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.

Author:
Alexandru Valeanu

  • Constructor Details

    • 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.
      Parameters:
      tree - the input tree
      root - the root of the tree

    • HeavyPathDecomposition

      public HeavyPathDecomposition(Graph<V,E> forest, 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.
      Parameters:
      forest - the input forest
      roots - the set of roots of the graph

  • Method Details