- Type Parameters:
V
- the graph vertex type.E
- the graph edge type.
MaximumCardinalityIterator
or LexBreadthFirstIterator
to compute a perfect
elimination order. The desired method is specified during construction time.
Chordal graphs are a subset of the perfect graphs. They may be recognized in polynomial time, and several problems that are hard on other classes of graphs such as minimum vertex coloring or determining maximum cardinality cliques and independent set can be performed in polynomial time when the input is chordal.
All methods in this class run in $\mathcal{O}(|V| + |E|)$ time. Determining whether a graph is
chordal, as well as computing a perfect elimination order takes $\mathcal{O}(|V| + |E|)$ time,
independent of the algorithm (MaximumCardinalityIterator
or
LexBreadthFirstIterator
) used to compute the perfect elimination order.
All the methods in this class are invoked in a lazy fashion, meaning that computations are only started once the method gets invoked.
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Nested Class Summary
Nested ClassesModifier and TypeClassDescriptionstatic enum
Specifies internal iterator type. -
Field Summary
FieldsModifier and TypeFieldDescriptionprivate boolean
Contains true if the graph is chordal, otherwise false.The inspected graph.A hole contained in the inspectedgraph
.private final ChordalityInspector.IterationOrder
Stores the type of iterator used by thisChordalityInspector
.Order produced byorderIterator
.private final GraphIterator
<V, E> Iterator used for producing perfect elimination order. -
Constructor Summary
ConstructorsConstructorDescriptionChordalityInspector
(Graph<V, E> graph) Creates a chordality inspector forgraph
, which usesMaximumCardinalityIterator
as a default iterator.ChordalityInspector
(Graph<V, E> graph, ChordalityInspector.IterationOrder iterationOrder) Creates a chordality inspector forgraph
, which uses an iterator defined by the second parameter as an internal iterator. -
Method Summary
Modifier and TypeMethodDescriptionprivate void
Computes some cycle in the graph on the vertices from the domain of the mapvisited
.private void
Computes a hole from the vertices ofsubgraph
of the inspectedgraph
with verticesa
,b
andc
on this cycle (there must be no edge betweena
andc
.getHole()
A graph which is not chordal, must contain a hole (chordless cycle on 4 or more vertices).Returns the type of iterator used in thisChordalityInspector
Returns a perfect elimination order if one exists.getPredecessors
(Map<V, Integer> vertexInOrder, V vertex) Returns the predecessors ofvertex
in the order defined bymap
.getVertexInOrder
(List<V> vertexOrder) Returns a map containing vertices from thevertexOrder
mapped to their indices invertexOrder
.boolean
Checks whether the inspected graph is chordal.boolean
isPerfectEliminationOrder
(List<V> vertexOrder) Checks whether the vertices in thevertexOrder
form a perfect elimination order with respect to the inspected graph.private boolean
isPerfectEliminationOrder
(List<V> vertexOrder, boolean computeHole) Checks whether the vertices in thevertexOrder
form a perfect elimination order with respect to the inspected graph.Computes vertex order viaorderIterator
.minimizeCycle
(List<V> cycle) Minimizes the cycle represented by the listcycle
.
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Field Details
-
iterationOrder
Stores the type of iterator used by thisChordalityInspector
. -
orderIterator
Iterator used for producing perfect elimination order. -
graph
The inspected graph. -
chordal
private boolean chordalContains true if the graph is chordal, otherwise false. -
order
Order produced byorderIterator
. -
hole
A hole contained in the inspectedgraph
.
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Constructor Details
-
ChordalityInspector
Creates a chordality inspector forgraph
, which usesMaximumCardinalityIterator
as a default iterator.- Parameters:
graph
- the graph for which a chordality inspector to be created.
-
ChordalityInspector
Creates a chordality inspector forgraph
, which uses an iterator defined by the second parameter as an internal iterator.- Parameters:
graph
- the graph for which a chordality inspector is to be created.iterationOrder
- the constant, which defines iterator to be used by thisChordalityInspector
.
-
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Method Details
-
isChordal
public boolean isChordal()Checks whether the inspected graph is chordal.- Returns:
- true if this graph is chordal, otherwise false.
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getPerfectEliminationOrder
Returns a perfect elimination order if one exists. The existence of a perfect elimination order certifies that the graph is chordal. This method returns null if the graph is not chordal.- Returns:
- a perfect elimination order of a graph or null if graph is not chordal.
-
getHole
A graph which is not chordal, must contain a hole (chordless cycle on 4 or more vertices). The existence of a hole certifies that the graph is not chordal. This method returns a chordless cycle if the graph is not chordal, or null if the graph is chordal.- Returns:
- a hole if the
graph
is not chordal, or null if the graph is chordal.
-
isPerfectEliminationOrder
Checks whether the vertices in thevertexOrder
form a perfect elimination order with respect to the inspected graph. Returns false otherwise.- Parameters:
vertexOrder
- the sequence of vertices of thegraph
.- Returns:
- true if the
graph
is chordal and the vertices invertexOrder
are in perfect elimination order, otherwise false.
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lazyComputeOrder
Computes vertex order viaorderIterator
.- Returns:
- computed order.
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isPerfectEliminationOrder
Checks whether the vertices in thevertexOrder
form a perfect elimination order with respect to the inspected graph. Returns false otherwise. Computes a hole if thecomputeHole
is true.- Parameters:
vertexOrder
- the sequence of vertices ofgraph
.computeHole
- tells whether to compute the hole if the graph isn't chordal.- Returns:
- true if the
graph
is chordal and the vertices invertexOrder
are in perfect elimination order.
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getVertexInOrder
Returns a map containing vertices from thevertexOrder
mapped to their indices invertexOrder
.- Parameters:
vertexOrder
- a list with vertices.- Returns:
- a mapping of vertices from
vertexOrder
to their indices invertexOrder
.
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findHole
Computes a hole from the vertices ofsubgraph
of the inspectedgraph
with verticesa
,b
andc
on this cycle (there must be no edge betweena
andc
.- Parameters:
a
- vertex that belongs to the cycleb
- vertex that belongs to the cyclec
- vertex that belongs to the cycle
-
dfsVisit
Computes some cycle in the graph on the vertices from the domain of the mapvisited
. More precisely, finds some path frommiddle
tofinish
. The vertexmiddle
isn't the endpoint of any chord in this cycle.- Parameters:
cycle
- already computed part of the cyclevisited
- the map that defines which vertex has been visited by this methodfinish
- the last vertex in the cycle.middle
- the vertex, which must be adjacent onlcurrent
- currently examined vertex.
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minimizeCycle
Minimizes the cycle represented by the listcycle
. More precisely it retains first 2 vertices and finds a chordless cycle starting from the third vertex.- Parameters:
cycle
- vertices of the graph that represent the cycle.- Returns:
- a chordless cycle
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getPredecessors
Returns the predecessors ofvertex
in the order defined bymap
. More precisely, returns those ofvertex
, whose mapped index inmap
is less then the index ofvertex
.- Parameters:
vertexInOrder
- defines the mapping of vertices ingraph
to their indices in order.vertex
- the vertex whose predecessors in order are to be returned.- Returns:
- the predecessors of
vertex
in order defines bymap
.
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getIterationOrder
Returns the type of iterator used in thisChordalityInspector
- Returns:
- the type of iterator used in this
ChordalityInspector
-