# An Effective Algorithm for and Phase Transitions of the Directed Hamiltonian Cycle Problem

@article{Jger2010AnEA, title={An Effective Algorithm for and Phase Transitions of the Directed Hamiltonian Cycle Problem}, author={Gerold J{\"a}ger and Weixiong Zhang}, journal={J. Artif. Intell. Res.}, year={2010}, volume={39}, pages={663-687} }

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… Expand

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#### References

SHOWING 1-10 OF 90 REFERENCES

The Gn,m Phase Transition is Not Hard for the Hamiltonian Cycle Problem

- Mathematics, Computer Science
- J. Artif. Intell. Res.
- 1998

Using an improved backtrack algorithm with sophisticated pruning techniques, we revise previous observations correlating a high frequency of hard to solve Hamiltonian cycle instances with the Gn,m… Expand

Efficient SAT Techniques for Absolute Encoding of Permutation Problems: Application to Hamiltonian Cycles

- Mathematics, Computer Science
- SARA
- 2009

Novel approaches for solving of hard combinatorial problems by translation to Boolean Satisfiability (SAT) by using the absolute SAT encoding of permutations, where for each of the n objects and each of its pos- sible positions in a permutation, a predicate is defined to indicate whether the object is placed in that position. Expand

An algorithm for finding hamilton paths and cycles in random graphs

- Mathematics
- 1987

This paper describes a polynomial time algorithm HAM that searches for Hamilton cycles in undirected graphs. On a random graph its asymptotic probability of success is that of the existence of such a… Expand

Digraphs - theory, algorithms and applications

- Computer Science
- 2002

Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science, and it will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology. Expand

A Study of Complexity Transitions on the Asymmetric Traveling Salesman Problem

- Mathematics, Computer Science
- Artif. Intell.
- 1996

It is shown experimentally that when the intercity distances of the asymmetric TSP are drawn uniformly from 0,1,2,…, r, the complexity of BnB experiences an easy-hard transition as r increases, and that the control parameter that determines the complexity is the number of distinct inter city distances. Expand

Efficient Conflict Analysis for Finding All Satisfying Assignments of a Boolean Circuit

- Computer Science, Mathematics
- TACAS
- 2005

An improved algorithm for finding all satisfying assignments for a generic Boolean circuit based on a hybrid SAT solver that can apply conflict analysis and implications to both CNF formulae and general circuits is presented. Expand

Determining computational complexity from characteristic ‘phase transitions’

- Computer Science
- Nature
- 1999

An analytic solution and experimental investigation of the phase transition in K -satisfiability, an archetypal NP-complete problem, is reported and the nature of these transitions may explain the differing computational costs, and suggests directions for improving the efficiency of search algorithms. Expand

Algorithm 595: An Enumerative Algorithm for Finding Hamiltonian Circuits in a Directed Graph

- Mathematics, Computer Science
- TOMS
- 1983

Let G = (V, A) be a directed graph (or digraph), where V {vl, v2 . . . . . v ,} is the set of the n ver t ices and A is the set o f the m arcs (v,, vj) in G. A Hamiltonian circuit in G is a p e r m u… Expand

Fast Probabilistic Algorithms for Hamiltonian Circuits and Matchings

- Computer Science, Mathematics
- J. Comput. Syst. Sci.
- 1979

Three simple efficient algorithms with good probabilistic behaviour are described and an algorithm with a run time of O ( n log n ) which almost certainly finds a perfect matching in a random graph of at least cn log n edges is analyzed. Expand

An Algorithm for Finding Hamilton Cycles in Random Directed Graphs

- Mathematics, Computer Science
- J. Algorithms
- 1988

A polynomial time algorithm DHAM for finding hamilton cycles in digraphs is described and some applications to random “travelling salesman problems” are discussed. Expand