Class ChordalGraphMinimalVertexSeparatorFinder<V,E>
 java.lang.Object

 org.jgrapht.alg.cycle.ChordalGraphMinimalVertexSeparatorFinder<V,E>

 Type Parameters:
V
 the graph vertex typeE
 the graph edge type
public class ChordalGraphMinimalVertexSeparatorFinder<V,E> extends Object
Allows obtaining a mapping of all minimal vertex separators of a graph to their multiplicitiesIn the context of this implementation following definitions are used:
 A set of vertices $S$ of a graph $G=(V, E)$ is called a uv separator, if vertices $u$ and $v$ in the induced graph on vertices $V(G)  S$ are in different connected components.
 A set $S$ is called a minimal uv separator if it is a uv separator and no proper subset of $S$ is a uv separator.
 A set $S$ is called a minimal vertex separator if it is minimal uv separator for some vertices $u$ and $v$ of the graph $G$.
 A set of vertices $S$ is called a minimal separator if no proper subset of $S$ is a separator of the graph $G$.
Let $\sigma = (v_1, v_2, \dots, v_n)$ be some perfect elimination order (peo) of the graph $G = (V, E)$. The induced graph on vertices $(v_1, v_2, \dots, v_i)$ with respect to peo $\sigma$ is denoted as $G_i$. The predecessors set of vertex $v$ with respect to peo $\sigma$ is denoted as $N(v, \sigma)$. A set $B$ is called a base set with respect to $\sigma$, is there exist some vertex $v$ with $t = \sigma(v)$ such that $N(v, \sigma) = B$ and B is not a maximal clique in $G_{t1}$. The vertices which satisfy conditions described above are called dependent vertices with respect to $\sigma$. The cardinality of the set of dependent vertices is called a multiplicity of the base set $B$. The multiplicity of a minimal vertex separator indicates the number of different pairs of vertices separated by it.The definitions of a base set and a minimal vertex separator in the context of chordal graphs are equivalent.
For more information on the topic see: Kumar, P. Sreenivasa & Madhavan, C. E. Veni. (1998). Minimal vertex separators of chordal graphs. Discrete Applied Mathematics. 89. 155168. 10.1016/S0166218X(98)001231.
The running time of the algorithm is $\mathcal{O}(\omega(G)(V + E))$, where $\omega(G)$ is the size of a maximum clique of the graph $G$.
 Author:
 Timofey Chudakov
 See Also:
ChordalityInspector


Constructor Summary
Constructors Constructor Description ChordalGraphMinimalVertexSeparatorFinder(Graph<V,E> graph)
Creates newChordalGraphMinimalVertexSeparatorFinder
instance.

Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description Set<Set<V>>
getMinimalSeparators()
Computes a set of all minimal separators of thegraph
and returns it.Map<Set<V>,Integer>
getMinimalSeparatorsWithMultiplicities()
Computes a mapping of all minimal vertex separators of thegraph
and returns it.



Constructor Detail

ChordalGraphMinimalVertexSeparatorFinder
public ChordalGraphMinimalVertexSeparatorFinder(Graph<V,E> graph)
Creates newChordalGraphMinimalVertexSeparatorFinder
instance. TheChordalityInspector
used in this implementation uses theMaximumCardinalityIterator
iterator Parameters:
graph
 the graph minimal separators to search in


Method Detail

getMinimalSeparators
public Set<Set<V>> getMinimalSeparators()
Computes a set of all minimal separators of thegraph
and returns it. Returns null if thegraph
isn't chordal. Returns:
 computed set of all minimal separators, or null if the
graph
isn't chordal

getMinimalSeparatorsWithMultiplicities
public Map<Set<V>,Integer> getMinimalSeparatorsWithMultiplicities()
Computes a mapping of all minimal vertex separators of thegraph
and returns it. Returns null if thegraph
isn't chordal. Returns:
 computed mapping of all minimal separators to their multiplicities, or null if the
graph
isn't chordal

