Class HeldKarpTSP<V,​E>

  • Type Parameters:
    V - the graph vertex type
    E - the graph edge type
    All Implemented Interfaces:

    public class HeldKarpTSP<V,​E>
    extends HamiltonianCycleAlgorithmBase<V,​E>
    A dynamic programming algorithm for the TSP problem.

    The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?".

    This is an implementation of the Held-Karp algorithm which returns a optimal, minimum-cost Hamiltonian tour. The implementation requires the input graph to contain at least one vertex. The running time is $O(2^{|V|} \times |V|^2)$ and it takes $O(2^{|V|} \times |V|)$ extra memory.

    See wikipedia for more details about TSP.

    See wikipedia for more details about the dynamic programming algorithm.

    Alexandru Valeanu
    • Constructor Detail

      • HeldKarpTSP

        public HeldKarpTSP()
    • Method Detail

      • getTour

        public GraphPath<V,​E> getTour​(Graph<V,​E> graph)
        Computes a minimum-cost Hamiltonian tour.
        graph - the input graph
        a minimum-cost tour if one exists, null otherwise
        java.lang.IllegalArgumentException - if the graph contains no vertices
        java.lang.IllegalArgumentException - if the graph contains more than 31 vertices