Class AbstractFundamentalCycleBasis<V,E>

Type Parameters:
V - the vertex type
E - the edge type
All Implemented Interfaces:
Direct Known Subclasses:
QueueBFSFundamentalCycleBasis, StackBFSFundamentalCycleBasis

public abstract class AbstractFundamentalCycleBasis<V,E> extends Object implements CycleBasisAlgorithm<V,E>
A base implementation for the computation of a fundamental cycle basis of a graph. Subclasses should only provide a method for constructing a spanning forest of the graph. A cycle basis is fundamental if and only if each cycle in the basis contains at least one edge which is not contained in any other cycle in the basis.

For information on algorithms and heuristics for the computation of fundamental cycle bases see the following paper: Narsingh Deo, G. Prabhu, and M. S. Krishnamoorthy. Algorithms for Generating Fundamental Cycles in a Graph. ACM Trans. Math. Softw. 8, 1, 26-42, 1982.

The implementation returns a fundamental cycle basis as an undirected cycle basis. For a discussion of different kinds of cycle bases in graphs see the following paper: Christian Liebchen, and Romeo Rizzi. Classes of Cycle Bases. Discrete Applied Mathematics, 155(3), 337-355, 2007.

Dimitrios Michail
  • Field Details

    • graph

      protected Graph<V,E> graph
  • Constructor Details

    • AbstractFundamentalCycleBasis

      public AbstractFundamentalCycleBasis(Graph<V,E> graph)
      graph - the input graph
  • Method Details

    • getCycleBasis

      public CycleBasisAlgorithm.CycleBasis<V,E> getCycleBasis()
      Return a list of cycles forming an undirected cycle basis of a graph.
      Specified by:
      getCycleBasis in interface CycleBasisAlgorithm<V,E>
      an undirected cycle basis
    • computeSpanningForest

      protected abstract Map<V,E> computeSpanningForest()
      Compute a spanning forest of the graph.

      The representation assumes that the map contains the predecessor edge of each vertex in the forest. The predecessor edge is the forest edge that was used to discover the vertex. If no such edge was used (the vertex is a leaf in the forest) then the corresponding entry must be null.

      a map representation of a spanning forest.