An algorithm for finding Hamilton paths and cycles in random graphs
Combinatorica - Theory of Computing
Finding Hamilton cycles in sparse random graphs
Journal of Combinatorial Theory Series A
An algorithm for finding Hamilton cycles in random directed graphs
Journal of Algorithms
Updating the Hamiltonian problem—a survey
Journal of Graph Theory
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Basic graph theory: paths and circuits
Handbook of combinatorics (vol. 1)
An efficient cost scaling algorithm for the assignment problem
Mathematical Programming: Series A and B
Bounds on the number of knight's tours
Discrete Applied Mathematics
Asymptotic and finite size parameters for phase transitions: Hamiltonian circuit as a case study
Information Processing Letters
Boosting combinatorial search through randomization
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Algorithms and codes for dense assignment problems: the state of the art
Discrete Applied Mathematics
Algorithm 595: An Enumerative Algorithm for Finding Hamiltonian Circuits in a Directed Graph
ACM Transactions on Mathematical Software (TOMS)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Nonsystematic Search and No-Good Learning
Journal of Automated Reasoning
Efficient conflict driven learning in a boolean satisfiability solver
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
SAT-Encodings, Search Space Structure, and Local Search Performance
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Constraint Processing
SAT problems with chains of dependent variables
Discrete Applied Mathematics - The renesse issue on satisfiability
Positional games on random graphs
Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
Graph theory: An algorithmic approach (Computer science and applied mathematics)
Graph theory: An algorithmic approach (Computer science and applied mathematics)
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
Efficient haplotype inference with boolean satisfiability
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
The Gn,mphase transition is not hard for the Hamiltonian cycle problem
Journal of Artificial Intelligence Research
Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Tolerance based contract-or-patch heuristic for the asymmetric TSP
CAAN'06 Proceedings of the Third international conference on Combinatorial and Algorithmic Aspects of Networking
Efficient conflict analysis for finding all satisfying assignments of a boolean circuit
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Certification of an optimal TSP tour through 85,900 cities
Operations Research Letters
| Hi-index | 0.00 |
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.