Class EsauWilliamsCapacitatedMinimumSpanningTree<V,​E>

  • Type Parameters:
    V - the vertex type
    E - the edge type
    All Implemented Interfaces:
    CapacitatedSpanningTreeAlgorithm<V,​E>

    public class EsauWilliamsCapacitatedMinimumSpanningTree<V,​E>
    extends AbstractCapacitatedMinimumSpanningTree<V,​E>
    Implementation of a randomized version of the Esau-Williams heuristic, a greedy randomized adaptive search heuristic (GRASP) for the capacitated minimum spanning tree (CMST) problem. It calculates a suboptimal CMST. The original version can be found in L. R. Esau and K. C. Williams. 1966. On teleprocessing system design: part II a method for approximating the optimal network. IBM Syst. J. 5, 3 (September 1966), 142-147. DOI=http://dx.doi.org/10.1147/sj.53.0142 This implementation runs in polynomial time O(|V|^3).

    This implementation is a randomized version described in Ahuja, Ravindra K., Orlin, James B., and Sharma, Dushyant, (1998). New neighborhood search structures for the capacitated minimum spanning tree problem, No WP 4040-98. Working papers, Massachusetts Institute of Technology (MIT), Sloan School of Management.

    This version runs in polynomial time dependent on the number of considered operations per iteration numberOfOperationsParameter (denoted by p), such that runs is in $O(|V|^3 + p|V|) = O(|V|^3)$ since $p \leq |V|$.

    A Capacitated Minimum Spanning Tree (CMST) is a rooted minimal cost spanning tree that satisfies the capacity constrained on all trees that are connected to the designated root. The problem is NP-hard.

    Since:
    July 12, 2018
    • Field Detail

      • numberOfOperationsParameter

        private final int numberOfOperationsParameter
        the number of the most profitable operations for every iteration considered in the procedure.
      • isAlgorithmExecuted

        private boolean isAlgorithmExecuted
        contains whether the algorithm was executed
    • Constructor Detail

      • EsauWilliamsCapacitatedMinimumSpanningTree

        public EsauWilliamsCapacitatedMinimumSpanningTree​(Graph<V,​E> graph,
                                                          V root,
                                                          double capacity,
                                                          java.util.Map<V,​java.lang.Double> weights,
                                                          int numberOfOperationsParameter)
        Constructs an Esau-Williams GRASP algorithm instance.
        Parameters:
        graph - the graph
        root - the root of the CMST
        capacity - the capacity constraint of the CMST
        weights - the weights of the vertices
        numberOfOperationsParameter - the parameter how many best vertices are considered in the procedure
    • Method Detail

      • getSolution

        protected AbstractCapacitatedMinimumSpanningTree.CapacitatedSpanningTreeSolutionRepresentation getSolution()
        Calculates a partition representation of the capacitated spanning tree. With that, it is possible to calculate the to the partition corresponding capacitated spanning tree in polynomial time by calculating the MSTs. The labels of the partition that are returned are non-negative.
        Returns:
        a representation of the partition of the capacitated spanning tree that has non-negative labels.
      • getListOfBestOptions

        private java.util.LinkedList<V> getListOfBestOptions​(java.util.Map<V,​java.lang.Double> savings)
        Returns the list of the best options as stored in savings.
        Parameters:
        savings - the savings calculated in the algorithm (see getSolution())
        Returns:
        the list of the numberOfOperationsParameter best options
      • calculateClosestVertex

        private V calculateClosestVertex​(V vertex,
                                         java.util.Map<V,​java.util.Set<java.lang.Integer>> restrictionMap,
                                         java.util.Map<java.lang.Integer,​V> shortestGate)
        Calculates the closest vertex to vertex such that the connection of vertex to the subtree of the closest vertex does not violate the capacity constraint and the savings are positive. Otherwise null is returned.
        Parameters:
        vertex - the vertex to find a valid closest vertex for
        restrictionMap - the set of labels of sets of the partition, in which the capacity constraint is violated.
        Returns:
        the closest valid vertex and null, if no valid vertex exists
      • getDistance

        private double getDistance​(V v1,
                                   V v2)