org.graphstream.algorithm
Class Kruskal

java.lang.Object
  org.graphstream.algorithm.AbstractSpanningTree
      org.graphstream.algorithm.Kruskal

All Implemented Interfaces:

Algorithm, SpanningTree

Direct Known Subclasses:

Prim

public class Kruskal
extends AbstractSpanningTree

Compute a spanning tree using the Kruskal algorithm.

Kruskal's algorithm is a greedy algorithm which allows to find a minimal spanning tree in a weighted connected graph. More informations on Wikipedia.

Example

The following example generates a graph with the Dorogovtsev-Mendes generator and then computes a spanning-tree using the Kruskal algorithm. The generator creates random weights for edges that will be used by the Kruskal algorithm. If no weight is present, algorithm considers that all weights are set to 1. When an edge is in the spanning tree, the algorithm will set its "ui.class" attribute to "intree", else the attribute is set to "notintree". According to the css stylesheet that is defined, spanning will be displayed with thick black lines while edges not in the spanning tree will be displayed with thin gray lines.

 import org.graphstream.graph.Graph;
 import org.graphstream.graph.implementations.DefaultGraph;
 
 import org.graphstream.algorithm.Kruskal;
 import org.graphstream.algorithm.generator.DorogovtsevMendesGenerator;
 
 public class KruskalTest {
  
        public static void main(String .. args) {
                DorogovtsevMendesGenerator gen = new DorogovtsevMendesGenerator();
                Graph graph = new DefaultGraph("Kruskal Test");
 
        String css = "edge .notintree {size:1px;fill-color:gray;} " +
                                 "edge .intree {size:3px;fill-color:black;}";
  
                graph.addAttribute("ui.stylesheet", css);
                graph.display();
 
                gen.addEdgeAttribute("weight");
                gen.setEdgeAttributesRange(1, 100);
                gen.addSink(graph);
                gen.begin();
                for (int i = 0; i < 100 && gen.nextEvents(); i++)
                        ;
                gen.end();
 
                Kruskal kruskal = new Kruskal("ui.class", "intree", "notintree");
 
                kruskal.init(g);
                kruskal.compute();
  }
 }
 

See Also:

AbstractSpanningTree

Computational Complexity :

O(m log n) where m is the number of edges and n is the number of nodes of the graph

Scientific Reference :

Joseph. B. Kruskal: On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem. In: Proceedings of the American Mathematical Society, Vol 7, No. 1 (Feb, 1956), pp. 48–50

Field Summary

static String

DEFAULT_WEIGHT_ATTRIBUTE Default weight attribute

Constructor Summary

Kruskal()
Create a new Kruskal's algorithm.

Kruskal(String flagAttribute, Object flagOn, Object flagOff)
Create a new Kruskal's algorithm.

Kruskal(String weightAttribute, String flagAttribute)
Create a new Kruskal's algorithm.

Kruskal(String weightAttribute, String flagAttribute, Object flagOn, Object flagOff)
Create a new Kruskal's algorithm.

Method Summary

void	clear() Removes the tags of all edges.
<T extends org.graphstream.graph.Edge> Iterator<T>	getTreeEdgesIterator() An iterator on the tree edges.
double	getTreeWeight() Returns the total weight of the minimum spanning tree
String	getWeightAttribute() Get weight attribute used to compare edges.
void	setWeightAttribute(String newWeightAttribute) Set the weight attribute.

Methods inherited from class org.graphstream.algorithm.AbstractSpanningTree

compute, getFlagAttribute, getFlagOff, getFlagOn, getTreeEdges, init, setFlagAttribute, setFlagOff, setFlagOn

Methods inherited from class java.lang.Object

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

Field Detail

DEFAULT_WEIGHT_ATTRIBUTE

public static final String DEFAULT_WEIGHT_ATTRIBUTE

Default weight attribute

See Also:

Constant Field Values

Constructor Detail

Kruskal

public Kruskal()

Create a new Kruskal's algorithm. Uses the default weight attribute and does not tag the edges.

Kruskal

public Kruskal(String weightAttribute,
               String flagAttribute)

Create a new Kruskal's algorithm. The value of the flag attribute is true for the tree edges and false for the non-tree edges.

Parameters:

weightAttribute - attribute used to compare edges

flagAttribute - attribute used to set if an edge is in the spanning tree

Kruskal

public Kruskal(String flagAttribute,
               Object flagOn,
               Object flagOff)

Create a new Kruskal's algorithm. Uses the default weight attribute.

Parameters:

flagAttribute - attribute used to set if an edge is in the spanning tree

flagOn - value of the flagAttribute if edge is in the spanning tree

flagOff - value of the flagAttribute if edge is not in the spanning tree

Kruskal

public Kruskal(String weightAttribute,
               String flagAttribute,
               Object flagOn,
               Object flagOff)

Create a new Kruskal's algorithm.

Parameters:

weightAttribute - attribute used to compare edges

flagAttribute - attribute used to set if an edge is in the spanning tree

flagOn - value of the flagAttribute if edge is in the spanning tree

flagOff - value of the flagAttribute if edge is not in the spanning tree

Method Detail

getWeightAttribute

public String getWeightAttribute()

Get weight attribute used to compare edges.

Returns:

weight attribute

setWeightAttribute

public void setWeightAttribute(String newWeightAttribute)

Set the weight attribute.

Parameters:

newWeightAttribute - new attribute used

getTreeEdgesIterator

public <T extends org.graphstream.graph.Edge> Iterator<T> getTreeEdgesIterator()

Description copied from interface: SpanningTree

An iterator on the tree edges.

Specified by:

getTreeEdgesIterator in interface SpanningTree

Specified by:

getTreeEdgesIterator in class AbstractSpanningTree

Returns:

An iterator on the tree edges

clear

public void clear()

Description copied from interface: SpanningTree

Removes the tags of all edges. Use this method to save memory if the spanning tree is used no more.

Specified by:

clear in interface SpanningTree

Overrides:

clear in class AbstractSpanningTree

getTreeWeight

public double getTreeWeight()

Returns the total weight of the minimum spanning tree

Returns:

The sum of the weights of the edges in the spanning tree