- Type Parameters:
V- the graph vertex type
E- the graph edge type
- All Implemented Interfaces:
public class PalmerHamiltonianCycle<V,E> extends Object implements HamiltonianCycleAlgorithm<V,E>Palmer's algorithm for computing Hamiltonian cycles in graphs that meet Ore's condition. Ore gave a sufficient condition for a graph to be Hamiltonian, essentially stating that a graph with sufficiently many edges must contain a Hamilton cycle. Specifically, Ore's theorem considers the sum of the degrees of pairs of non-adjacent vertices: if every such pair has a sum that at least equals the total number of vertices in the graph, then the graph is Hamiltonian.
A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node exactly once (Skiena 1990, p. 196).
This is an implementation of the algorithm described by E. M. Palmer in his paper. The algorithm takes a simple graph that meets Ore's condition (see
GraphTests.hasOreProperty(Graph)) and returns a Hamiltonian cycle. The algorithm runs in $O(|V|^2)$ time and uses $O(|V|)$ space.
The original algorithm is described in: Palmer, E. M. (1997), "The hidden algorithm of Ore's theorem on Hamiltonian cycles", Computers & Mathematics with Applications, 34 (11): 113–119, doi:10.1016/S0898-1221(97)00225-3 See wikipedia for a short description of Ore's theorem and Palmer's algorithm.
- Alexandru Valeanu
Constructors Constructor Description
PalmerHamiltonianCycle()Construct a new instance
All Methods Instance Methods Concrete Methods Modifier and Type Method Description
getTour(Graph<V,E> graph)Computes a Hamiltonian tour.
getTourComputes a Hamiltonian tour.