Related papers: Random Constraint Satisfaction Problems
The Random Satisfiability problem has been intensively studied for decades. For a number of reasons the focus of this study has mostly been on the model, in which instances are sampled uniformly at random from a set of formulas satisfying…
In this paper, we analyze the decision version of the NK landscape model from the perspective of threshold phenomena and phase transitions under two random distributions, the uniform probability model and the fixed ratio model. For the…
Despite significant advances in characterizing the highly nonconvex landscapes of constraint satisfaction problems, the good performance of certain algorithms in solving hard combinatorial optimization tasks remains poorly understood. This…
In a broad class of sparse random constraint satisfaction problems(CSP), deep heuristics from statistical physics predict that there is a condensation phase transition before the satisfiability threshold, governed by one-step replica…
This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of…
This paper presents a deterministic algorithmic approach of exploring the solution space of the Subset Sum Problem. The algorithm presented is input-robust and structurally adaptive. Exploration is guided and narrows into areas in the…
We focus on the random generation of SAT instances that have properties similar to real-world instances. It is known that many industrial instances, even with a great number of variables, can be solved by a clever solver in a reasonable…
We consider random systems of equations x_1 + ... + x_k = a; 0 <= a <= 2 which are interpreted as equations modulo 3: We show for k >= 15 that the satisfiability threshold of such systems occurs where the 2-core has density 1: We show a…
The QSAT problem is the quantified version of the SAT problem. We show the existence of a threshold effect for the phase transition associated with the satisfiability of random quantified extended 2-CNF formulas. We consider boolean CNF…
The exponential-time hypothesis (ETH) states that 3-SAT is not solvable in subexponential time, i.e. not solvable in O(c^n) time for arbitrary c > 1, where n denotes the number of variables. Problems like k-SAT can be viewed as special…
A constraint satisfaction problem (CSP) is said to be \emph{approximation resistant} if it is hard to approximate better than the trivial algorithm which picks a uniformly random assignment. Assuming the Unique Games Conjecture, we give a…
The distribution of overlaps of solutions of a random CSP is an indicator of the overall geometry of its solution space. For random $k$-SAT, nonrigorous methods from Statistical Physics support the validity of the ``one step replica…
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…
Local consistency techniques such as k-consistency are a key component of specialised solvers for constraint satisfaction problems. In this paper we show that the power of using k-consistency techniques on a constraint satisfaction problem…
We compute the probability of satisfiability of a class of random Horn-SAT formulae, motivated by a connection with the nonemptiness problem of finite tree automata. In particular, when the maximum clause length is 3, this model displays a…
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…
We study the behavior of ASAT, a heuristic for solving satisfiability problems by stochastic local search near the SAT/UNSAT transition. The heuristic is focused, i.e. only variables in unsatisfied clauses are updated in each step, and is…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
We revisit the so-called sampling and discarding approach used to quantify the probability of constraint violation of a solution to convex scenario programs when some of the original samples are allowed to be discarded. Motivated by two…
With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness…