Finding Hamiltonian Cycles: Algorithms, Graphs and Performance
Basil Vandegriend Masters Thesis February 1998.
Postscript available here
Source Code for HC algorithms here
My Master's thesis "Finding Hamiltonian Cycles: Algorithms, Graphs
and Performance" deals with the Hamiltonian cycle problem, an NP-C
problem in graph theory. The problem consists of finding a tour (or cycle)
that visits all the vertices once and returns to the starting vertex.
I have investigated several related issues:
- Design issues for backtrack Hamiltonian cycle algorithms
- Design issues for heuristic Hamiltonian cycle algorithms
- Generalizations of the knight's tour problem (a subset of the
Hamiltonian cycle problem).
- Hard regions of the Hamiltonian cycle problem. My goal here is to
identify graphs and graph properties that make the Hamiltonian cycle
problem hard or that distinguish between various Hamiltonian cycle
algorithms. I have focused mainly on low degree randomized graphs.