An Improved Exact Algorithm for the Domatic Number Problem

@article{Riege2006AnIE,
  title={An Improved Exact Algorithm for the Domatic Number Problem},
  author={Tobias Riege and J{\"o}rg Rothe and Holger Spakowski and Masaki Yamamoto},
  journal={2006 2nd International Conference on Information \& Communication Technologies},
  year={2006},
  volume={2},
  pages={2792-2797}
}
  • Tobias Riege, J. Rothe, Masaki Yamamoto
  • Published 16 March 2006
  • Computer Science, Mathematics
  • 2006 2nd International Conference on Information & Communication Technologies

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References

SHOWING 1-10 OF 30 REFERENCES
An Exact 2.9416n Algorithm for the Three Domatic Number Problem
TLDR
This paper designs an exact deterministic algorithm that can handle problem instances of larger size than the naive algorithm in the same amount of time and presents another deterministic and a randomized algorithm for this problem that both have even better performance for graphs with small maximum degree.
Improved upper bounds for 3-SAT
TLDR
For small k’s, especially for k = 3, there exists a lot of algorithms which run significantly faster than the trivial 2 bound, the following list summarizes those algorithms where a constant c means that the algorithm runs in time O(c).
An improved exponential-time algorithm for k-SAT
TLDR
It is shown that, for each k, the running time of ResolveSat on a k-CNF formula is significantly better than 2/sup n/, even in the worst case, and the idea of succinctly encoding satisfying solutions can be applied to obtain lower bounds on circuit site.
Complexity of the Exact Domatic Number Problem and of the Exact Conveyor Flow Shop Problem
  • Tobias Riege, J. Rothe
  • Mathematics
    Proceedings. 2004 International Conference on Information and Communication Technologies: From Theory to Applications, 2004.
  • 2004
TLDR
It is proved that the exact versions of the domatic number problem are complete for the levels of the Boolean hierarchy over NP, the 2kth level of the boolean hierarchy overNP.
Approximating the domatic number
TLDR
D domatic number is made the first natural maximization problem (known to the authors) that is provably approximable to within polylogarithmic factors but no better.
A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems
TLDR
This analysis shows that for any satisfiable k-CNF formula with n variables this process has to be repeated only t times, on the average, to find a satisfying assignment, where t is within a polynomial factor of(2(1 1=k)).
Algorithmics in Exponential Time
TLDR
The purpose of the current paper is to show cases in which the constant c could be significantly reduced, and to point out that there are some randomized exponential-time algorithms which use randomization in some new ways.
Measure and Conquer: Domination - A Case Study
TLDR
Davis-Putnam-style exponential-time backtracking algorithms are the most common algorithms used for finding exact solutions of NP-hard problems; the running time of these algorithms is largely overestimated because of a “bad” choice of the measure.
A Probabilistic Algorithm for k -SAT Based on Limited Local Search and Restart
TLDR
The analysis shows that for any satisfiable k -CNF formula with n variables the expected number of repetitions until a satisfying assignment is found this way is (2⋅ (k-1)/ k)n, and the algorithm presented here has a complexity which is within a polynomial factor of (\frac 4 3 )n .
...
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