An Effective Algorithm for and Phase Transitions of the Directed
  Hamiltonian Cycle Problem
  The Hamiltonian cycle problem (HCP) is an important combinatorial problem
with applications in many areas. It is among the first problems used for
studying intrinsic properties, including phase transitions, of combinatorial
problems. While thorough theoretical and experimental analyses have been made
on the HCP in undirected graphs, a limited amount of work has been done for the
HCP in directed graphs (DHCP). The main contribution of this work is an
effective algorithm for the DHCP. Our algorithm explores and exploits the close
relationship between the DHCP and the Assignment Problem (AP) and utilizes a
technique based on Boolean satisfiability (SAT). By combining effective
algorithms for the AP and SAT, our algorithm significantly outperforms previous
exact DHCP algorithms, including an algorithm based on the award-winning
Concorde TSP algorithm. The second result of the current study is an
experimental analysis of phase transitions of the DHCP, verifying and refining
a known phase transition of the DHCP.
