Class HowardMinimumMeanCycle<V,E>

java.lang.Object
org.jgrapht.alg.cycle.HowardMinimumMeanCycle<V,E>
Type Parameters:
V - graph vertex type
E - graph edge type
All Implemented Interfaces:
MinimumCycleMeanAlgorithm<V,E>
public class HowardMinimumMeanCycle<V,E> extends Object implements MinimumCycleMeanAlgorithm<V,E>
Implementation of Howard`s algorithm for finding minimum cycle mean in a graph.

The algorithm is described in the article: Ali Dasdan, Sandy S. Irani, and Rajesh K. Gupta. 1999. Efficient algorithms for optimum cycle mean and optimum cost to time ratio problems. In Proceedings of the 36th annual ACM/IEEE Design Automation Conference (DAC ’99). Association for Computing Machinery, New York, NY, USA, 37–42. DOI:https://doi.org/10.1145/309847.309862

Firstly, the graph is divided into strongly connected components. The minimum cycle mean is then computed as the globally minimum cycle mean over all components. In the process the necessary information is recorded to be able to reconstruct the cycle with minimum mean.

The computations are divided into iterations. In each iteration the algorithm tries to update current minimum cycle mean value. There is a possibility to limit the total number of iteration via a constructor parameter.

  • Field Details

    • graph

      private final Graph<V,E> graph
      The underlying graph.

    • strongConnectivityAlgorithm

      private final StrongConnectivityAlgorithm<V,E> strongConnectivityAlgorithm
      Algorithm for computing strongly connected components in the graph.

    • maximumIterations

      private final int maximumIterations
      Maximum number of iterations performed during the computation. If not provided via constructor the value if defaulted to Integer.MAX_VALUE.

    • comparator

      private final Comparator<Double> comparator
      Used to compare floating point numbers.

    • isCurrentCycleFound

      private boolean isCurrentCycleFound
      Determines if a cycle is found on current iteration.

    • currentCycleWeight

      private double currentCycleWeight
      Total weight of a cycle found on current iteration.

    • currentCycleLength

      private int currentCycleLength
      Length of a cycle found on current iteration.

    • currentCycleVertex

      private V currentCycleVertex
      Vertex which is used to reconstruct the cycle found on current iteration.

    • policyGraph

      private Map<V,E> policyGraph
      For each vertex contains an edge, which together for the policy graph on current iteration.

    • reachedVertices

      private Map<V,Boolean> reachedVertices
      For each vertex indicates, if it has been reached by a search during computing vertices distance in the policy graph.

    • vertexLevel

      private Map<V,Integer> vertexLevel
      For each vertex stores its level which is used to find a cycle in the policy graph.

    • vertexDistance

      private Map<V,Double> vertexDistance
      For each vertex stores its distance in the policy graph.

  • Constructor Details

    • HowardMinimumMeanCycle

      public HowardMinimumMeanCycle(Graph<V,E> graph)
      Constructs an instance of the algorithm for the given graph.
      Parameters:
      graph - graph

    • HowardMinimumMeanCycle

      public HowardMinimumMeanCycle(Graph<V,E> graph, int maximumIterations)
      Constructs an instance of the algorithm for the given graph and maximumIterations.
      Parameters:
      graph - graph
      maximumIterations - maximum number of iterations

    • HowardMinimumMeanCycle

      public HowardMinimumMeanCycle(Graph<V,E> graph, int maximumIterations, StrongConnectivityAlgorithm<V,E> strongConnectivityAlgorithm, double toleranceEpsilon)
      Constructs an instance of the algorithm for the given graph, maximumIterations, strongConnectivityAlgorithm and toleranceEpsilon.
      Parameters:
      graph - graph
      maximumIterations - maximum number of iterations
      strongConnectivityAlgorithm - algorithm to compute strongly connected components
      toleranceEpsilon - tolerance to compare floating point numbers

  • Method Details

    • getCycleMean

      public double getCycleMean()
      Computes minimum mean among all cycle. Returns Double.POSITIVE_INFINITY if no cycle has been found.
      Specified by:
      getCycleMean in interface MinimumCycleMeanAlgorithm<V,E>
      Returns:
      minimum mean

    • getCycle

      public GraphPath<V,E> getCycle()
      Computes cycle with minimum mean. Returns $null$ if no cycle has been found.
      Specified by:
      getCycle in interface MinimumCycleMeanAlgorithm<V,E>
      Returns:
      cycle with minimum mean

    • constructPolicyGraph

      private void constructPolicyGraph(Graph<V,E> component)
      Computes policy graph for component and stores result in policyGraph and vertexDistance. For every vertex in the policy graph an edge with the minimum weight is retained in the policy graph.
      Parameters:
      component - connected component

    • constructCycle

      private void constructCycle(Graph<V,E> component)
      Finds cycle in the policyGraph and computes computes its mean. The found cycle is identified by a vertex currentCycleVertex. The cycle returned by this method does not necessarily has the smalles mean over all cycles in the policy graph.

      To find cycles this methods assigns a level to each vertex. Initially every vertex has a level equal to $-1$ which means that the vertex has not been visited. During the computations this method starts DFS from every not visited vertex and assigns a unique positive level $l$ to every traversed vertex. If DFS comes across a vertex with level $l$ this indicates that a cycle has been detected.

      Parameters:
      component - connected component

    • computeVertexDistance

      private boolean computeVertexDistance(Graph<V,E> component)
      This method runs the reverted BFS starting from currentCycleVertex to update data in policyGraph and vertexDistance. This step is needed to identify if current value of minimum mean is optimal for the graph. This method also uses comparator to find out if update value of minium mean is sufficiently smaller than the previous one.
      Parameters:
      component - connected component
      Returns:
      if the currently best mean has been improved

    • buildPath

      private GraphPath<V,E> buildPath(V bestCycleVertex, int bestCycleLength, double bestCycleWeight)
      Constructs cycle with minimum mean using information in policyGraph.
      Parameters:
      bestCycleVertex - cycle vertex
      bestCycleLength - cycle length
      bestCycleWeight - cycle weight
      Returns:
      constructed minimum mean cycle