Class BoyerMyrvoldPlanarityInspector<V,E>
- java.lang.Object
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- org.jgrapht.alg.planar.BoyerMyrvoldPlanarityInspector<V,E>
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- Type Parameters:
V
- the graph vertex typeE
- the graph edge type
- All Implemented Interfaces:
PlanarityTestingAlgorithm<V,E>
public class BoyerMyrvoldPlanarityInspector<V,E> extends java.lang.Object implements PlanarityTestingAlgorithm<V,E>
An implementation of the Boyer-Myrvold planarity testing algorithm. This class determines whether an input graph is planar or not. If the graph is planar, the algorithm provides a combinatorial embedding of the graph, which is represented as a clockwise ordering of the edges of the graph. Otherwise, the algorithm provides a Kuratowski subgraph as a certificate. Both embedding of the graph and Kuratowski subdivision are computed lazily, meaning that the call to theisPlanar()
does spend time only on the planarity testing. All of the operations of this algorithm (testing, embedding and Kuratowski subgraph extraction) run in linear time.A planar graph is a graph, which can be drawn in two-dimensional space without any of its edges crossing. According to the Kuratowski theorem, a graph is planar if and only if it doesn't contain a subdivision of the $K_{3,3}$ or $K_{5}$ graphs.
The Boyer-Myrvold planarity testing algorithm was originally described in: Boyer, John amp; Myrvold, Wendy. (2004). On the Cutting Edge: Simplified O(n) Planarity by Edge Addition. J. Graph Algorithms Appl.. 8. 241-273. 10.7155/jgaa.00091. . We refer to this paper for the complete description of the Boyer-Myrvold algorithm
- Author:
- Timofey Chudakov
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Nested Class Summary
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Nested classes/interfaces inherited from interface org.jgrapht.alg.interfaces.PlanarityTestingAlgorithm
PlanarityTestingAlgorithm.Embedding<V,E>, PlanarityTestingAlgorithm.EmbeddingImpl<V,E>
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Constructor Summary
Constructors Constructor Description BoyerMyrvoldPlanarityInspector(Graph<V,E> graph)
Creates new instance of the planarity testing algorithm for thegraph
.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description PlanarityTestingAlgorithm.Embedding<V,E>
getEmbedding()
Computes combinatorial embedding of the inputgraph
.Graph<V,E>
getKuratowskiSubdivision()
Extracts a Kuratowski subdivision from thegraph
.boolean
isPlanar()
Tests the planarity of thegraph
.
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Method Detail
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isPlanar
public boolean isPlanar()
Tests the planarity of thegraph
. Returns true if the input graph is planar, false otherwise. If this method returns true, the combinatorial embedding of thegraph
is provided after the call to thePlanarityTestingAlgorithm.getEmbedding()
. Otherwise, a Kuratowski subdivision is provided after the call to thePlanarityTestingAlgorithm.getKuratowskiSubdivision()
.Only the first call to this method does the actual computation, all subsequent calls only return the previously computed value.
- Specified by:
isPlanar
in interfacePlanarityTestingAlgorithm<V,E>
- Returns:
true
if thegraph
is planar, false otherwise
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getEmbedding
public PlanarityTestingAlgorithm.Embedding<V,E> getEmbedding()
Computes combinatorial embedding of the inputgraph
. This method will return a valid result only if thegraph
is planar. For more information on the combinatorial embedding, seePlanarityTestingAlgorithm.Embedding
Only the first call to this method does the actual computation, all subsequent calls only return the previously computed value.
- Specified by:
getEmbedding
in interfacePlanarityTestingAlgorithm<V,E>
- Returns:
- combinatorial embedding of the input
graph
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getKuratowskiSubdivision
public Graph<V,E> getKuratowskiSubdivision()
Extracts a Kuratowski subdivision from thegraph
. The returned value certifies the nonplanarity of the graph. The returned certificate can be verified through the call to theGraphTests.isKuratowskiSubdivision(Graph)
. This method will return a valid result only if thegraph
is not planar.Only the first call to this method does the actual computation, all subsequent calls only return the previously computed value.
- Specified by:
getKuratowskiSubdivision
in interfacePlanarityTestingAlgorithm<V,E>
- Returns:
- a Kuratowski subdivision from the
graph
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