A probabilistic algorithm for k-SAT and constraint satisfaction problems

@article{Schoning1999APA,
  title={A probabilistic algorithm for k-SAT and constraint satisfaction problems},
  author={Torsten Schoning},
  journal={40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)},
  year={1999},
  pages={410-414}
}
  • T. Schoning
  • Published 17 October 1999
  • Computer Science
  • 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)
We present a simple probabilistic algorithm for solving k-SAT and more generally, for solving constraint satisfaction problems (CSP). The algorithm follows a simple local search paradigm (S. Minton et al., 1992): randomly guess an initial assignment and then, guided by those clauses (constraints) that are not satisfied, by successively choosing a random literal from such a clause and flipping the corresponding bit, try to find a satisfying assignment. If no satisfying assignment is found after… 

PPZ For More Than Two Truth Values - An Algorithm for Constraint Satisfaction Problems

To analyze the so-called ppz algorithm for (d,k)-CSP problems for general values of d and k, and to prove a correlation inequality for submodular functions, the algorithm is analyzed.

Improved upper bounds for 3-SAT

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).

Algorithms for Sat and Upper Bounds on Their Complexity

We survey recent algorithms for the propositional satisfiability problem. In particular, we consider algorithms having the best current worst-case upper bounds on their complexity. We also discuss

Bridging between 0/1 and linear programming via random walks

This work gives a natural algorithmic bridging between these extremes of 0-1 and linear programming by giving a random-walk based algorithm with runtime OE((2−measure(E)npoly(n,m))) that finds a solution in En to any n-variable linear program with m constraints that is feasible over {0,1}n.

WALCOM: Algorithms and Computation

Results about the difficulty and approximability of a single-facility location for general networks and polynomial time algorithms for k-facilities location problems in path and tree networks and multi-commodity dynamic flow problems are shown.

Relaxed Random Search for Solving K-Satisfiability and its Information Theoretic Interpretation

It is shown how the probability of literal flipping process can change the complexity of algorithm substantially and an information theoretic interpretation of this reduction in time complexity will be argued.

Randomized algorithm for informative path planning with budget constraints

  • S. AroraS. Scherer
  • Computer Science
    2017 IEEE International Conference on Robotics and Automation (ICRA)
  • 2017
The key idea of the approach is to pose orienteering as a combination of a Constraint Satisfaction Problem and a Traveling Salesman Problem, which allows for an improvement by an order of magnitude over the state of the art methods in relevant simulation and in real world scenarios.

Probabilistic algorithm for determining bit multipliers in the problem of factoring Integers

  • Y. Ogorodnikov
  • Computer Science, Mathematics
    2015 International Siberian Conference on Control and Communications (SIBCON)
  • 2015
A probabilistic algorithm for determining the bit multipliers in the problem of factoring integers, the most famous application of which is the use of the algorithm RSA, which is based on the reduction of factorization problem to the issue of satisfiability of Boolean formulas.

Novel Analysis of Transition Probabilities in Randomized K-Sat Algorithm

A new analysis for randomized 2-SAT and 3-S AT algorithms is proposed, and it is shown that more precise boundaries for transition probability of Markov chain using Karnaugh map could be determined.

Derandomizing HSSW Algorithm for 3-SAT

A (full) derandomization of HSSW algorithm for 3-SAT is presented and an O(1.3303n)-time deterministic algorithm is obtained, which is currently fastest.
...

References

SHOWING 1-10 OF 15 REFERENCES

An Introduction to Probability Theory and Its Applications

Thank you for reading an introduction to probability theory and its applications vol 2. As you may know, people have look numerous times for their favorite novels like this an introduction to

Solving 3-Satisfiability in Less Then 1, 579n Steps

This paper describes and analyse an improved algorithm for solving the 3-Satisfiability problem and shows that this algorithm solves the Satisfiability problem for formulas with at most three literals per clause in time less than O(1,579n).

Satisfiability - Algorithms and Logic

Some results in proof complexity that can be used to derive lower bounds on classes of algorithms for satisfiability of k-CNF formulas are mentioned.

Deciding 3-Colourability in Less Than O(1.415^n) Steps

An improved algorithm for deciding the 3-Colourability problem is described and analyzed and it is shown that this algorithm tests a graph for 3- Colourability, i.e. an assignment of three colours to the vertices of G such that two adjacent vertices obtain different colours, in less than O(1.415n) steps.

Search methods for artificial intelligence

Surveys a variety of search methods for problem-solving in terms of the sorts of problems that arise in the development of artificial intelligence. The theoretical and practical implications of a

Randomized Algorithms

This book introduces the basic concepts in the design and analysis of randomized algorithms and presents basic tools such as probability theory and probabilistic analysis that are frequently used in algorithmic applications.

Algorithms and Theory of Computation Handbook

  • M. Atallah
  • Computer Science
    Chapman & Hall/CRC Applied Algorithms and Data Structures series
  • 1999
This edition now covers external memory, parameterized, self-stabilizing, and pricing algorithms as well as the theories of algorithmic coding, privacy and anonymity, databases, computational games, and communication networks.

On selecting a satisfying truth assignment

  • C. Papadimitriou
  • Mathematics
    [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science
  • 1991
The complexity of certain natural generalizations of satisfiability, in which one of the possibly exponentially many satisfying truth assignments must be selected, is studied and yields a new and very natural polynomial-time randomized algorithm for 2SAT.

Satisfiability Coding Lemma

This basic lemma shows how to encode satisfying solutions of a /spl kappa/-CNF succinctly as well as an upper and lower bound on the size of depth 3 circuits of AND and OR gates computing the parity function.