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
Incremental SAT-Based Method with Native Boolean Cardinality Handling for the Hamiltonian Cycle Problem
TLDR
This paper proposes an incremental SAT-based method for solving the Hamiltonian cycle problem by relaxing some constraints and by handling specifically cardinality constraints. Expand
Empirical Study of Phase Transition of Hamiltonian Cycle Problem in Random Graphs with Degrees Greater Than One
TLDR
This paper proves that random graphs with such critical average node degrees tend to be hamiltonian graphs if their node degrees are greater than one, and demonstrates that hard cases can be found with high probability when graphs take lower average degrees. Expand
SAT and IP based algorithms for magic labeling including a complete search for total magic labelings
TLDR
An exhaustive search showing that no totally magic graph with 11 vertices exists is performed, and effective IP and Sat based algorithms for finding a magic labeling for a given graph are presented and extended to find all magic labelings for aGiven graph. Expand
SAT and IP Based Algorithms for Magic Labeling with Applications
  • G. Jäger
  • Mathematics, Computer Science
  • IWOCA
  • 2013
TLDR
This work presents effective IP and Sat based algorithms for the problem of finding a magic labeling for a given graph and demonstrates its performance by solving five open problems within the theory of magic graphs. Expand
SAT Encodings of Finite CSPs
TLDR
This thesis studies SAT encodings of CSPs by conducting a comprehensively profound study and revealing interesting guidelines on how to choose an appropriate SAT encoding in the way that one can exploit the availability of many efficient SAT solvers to solve C SPs efficiently and effectively. Expand
The complete parsimony haplotype inference problem and algorithms based on integer programming, branch-and-bound and Boolean satisfiability
TLDR
The problem of Hipp is generalized to the problem of finding all optimal solutions, which is called Chipp, and intrinsic haplotype features, such as backbone haplotypes and fat genotypes as well as equal columns and decomposability are studied. Expand
Where the really hard problems aren’t
TLDR
A new contradiction renders the earlier proposed order parameter unsuitable and changes the perspective on the fundamentals of ATSP instance hardness for this kind of algorithm, which gives rise to a sudden emergence of minimum-cost tours. Expand

References

SHOWING 1-10 OF 90 REFERENCES
The Gn,m Phase Transition is Not Hard for the Hamiltonian Cycle Problem
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,mExpand
Efficient SAT Techniques for Absolute Encoding of Permutation Problems: Application to Hamiltonian Cycles
TLDR
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
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 aExpand
Digraphs - theory, algorithms and applications
TLDR
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
TLDR
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
TLDR
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’
TLDR
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
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 uExpand
Fast Probabilistic Algorithms for Hamiltonian Circuits and Matchings
TLDR
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
  • A. Frieze
  • Mathematics, Computer Science
  • J. Algorithms
  • 1988
TLDR
A polynomial time algorithm DHAM for finding hamilton cycles in digraphs is described and some applications to random “travelling salesman problems” are discussed. Expand
...
1
2
3
4
5
...