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

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
class	HeavyPathDecomposition.InternalState Internal representation of the data

Nested classes/interfaces inherited from interface org.jgrapht.alg.interfaces.TreeToPathDecompositionAlgorithm

TreeToPathDecompositionAlgorithm.PathDecomposition<V,E>, TreeToPathDecompositionAlgorithm.PathDecompositionImpl<V,E>

Constructor Summary

Constructors

Constructor and Description
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).
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.

Method Summary

Modifier and Type	Method and Description
Set<E>	getHeavyEdges() Set of heavy edges.
HeavyPathDecomposition.InternalState	getInternalState() Return the internal representation of the data.
Set<E>	getLightEdges() Set of light edges.
TreeToPathDecompositionAlgorithm.PathDecomposition<V,E>	getPathDecomposition() Computes a path decomposition.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

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.

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 Detail

getHeavyEdges

public Set<E> getHeavyEdges()

Set of heavy edges.

Returns:

(immutable) set of heavy edges

getLightEdges

public Set<E> getLightEdges()

Set of light edges.

Returns:

(immutable) set of light edges

getPathDecomposition

public TreeToPathDecompositionAlgorithm.PathDecomposition<V,E> getPathDecomposition()

Computes a path decomposition.

Specified by:

getPathDecomposition in interface TreeToPathDecompositionAlgorithm<V,E>

Returns:

a path decomposition

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

Returns:

the internal state representation