On the survey-propagation equations in random constraint satisfiability problems

2008 ◽  
Vol 49 (12) ◽  
pp. 125216 ◽  
Author(s):  
Giorgio Parisi
Keyword(s):  
Satisfiability Problems ◽  
Survey Propagation ◽  
Constraint Satisfiability

scholarly journals Better Algorithms for Satisfiability Problems for Formulas of Bounded Rank-width

2013 ◽  
Vol 123 (1) ◽  
pp. 59-76 ◽  
Author(s):  
Robert Ganian ◽  
Petr Hliněný ◽  
Jan Obdržálek
Keyword(s):  
Satisfiability Problems ◽  
Bounded Rank

scholarly journals Constraint Satisfaction by Survey Propagation

2005 ◽  
Author(s):  
Alfredo Braunstein ◽  
Marc Mézard
Keyword(s):  
Constraint Satisfaction ◽  
Message Passing ◽  
Statistical Physics ◽  
Belief Propagation ◽  
Solution Space ◽  
Error Correcting Codes ◽  
Constraint Satisfaction Problems ◽  
Probabilistic Methods ◽  
Survey Propagation ◽  
Algorithmic Strategy

Methods and analyses from statistical physics are of use not only in studying the performance of algorithms, but also in developing efficient algorithms. Here, we consider survey propagation (SP), a new approach for solving typical instances of random constraint satisfaction problems. SP has proven successful in solving random k-satisfiability (k -SAT) and random graph q-coloring (q-COL) in the “hard SAT” region of parameter space [79, 395, 397, 412], relatively close to the SAT/UNSAT phase transition discussed in the previous chapter. In this chapter we discuss the SP equations, and suggest a theoretical framework for the method [429] that applies to a wide class of discrete constraint satisfaction problems. We propose a way of deriving the equations that sheds light on the capabilities of the algorithm, and illustrates the differences with other well-known iterative probabilistic methods. Our approach takes into account the clustered structure of the solution space described in chapter 3, and involves adding an additional “joker” value that variables can be assigned. Within clusters, a variable can be frozen to some value, meaning that the variable always takes the same value for all solutions (satisfying assignments) within the cluster. Alternatively, it can be unfrozen, meaning that it fluctuates from solution to solution within the cluster. As we will discuss, the SP equations manage to describe the fluctuations by assigning joker values to unfrozen variables. The overall algorithmic strategy is iterative and decomposable in two elementary steps. The first step is to evaluate the marginal probabilities of frozen variables using the SP message-passing procedure. The second step, or decimation step, is to use this information to fix the values of some variables and simplify the problem. The notion of message passing will be illustrated throughout the chapter by comparing it with a simpler procedure known as belief propagation (mentioned in ch. 3 in the context of error correcting codes) in which no assumptions are made about the structure of the solution space. The chapter is organized as follows. In section 2 we provide the general formalism, defining constraint satisfaction problems as well as the key concepts of factor graphs and cavities, using the concrete examples of satisfiability and graph coloring.

scholarly journals On the Performance of Congestion Games for Optimum Satisfiability Problems

2007 ◽  
pp. 220-231 ◽  
Author(s):  
Aristotelis Giannakos ◽  
Laurent Gourvès ◽  
Jérôme Monnot ◽  
Vangelis Th. Paschos
Keyword(s):  
Congestion Games ◽  
Satisfiability Problems
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