Related papers: Sharp thresholds for constraint satisfaction probl…
The model of Dynamic Meta-Constraints has special activity constraints which can activate other constraints. It also has meta-constraints which range over other constraints. An algorithm is presented in which constraints can be assigned one…
In this paper we provide an extended formulation for the class of constraint satisfaction problems and prove that its size is polynomial for instances whose constraint graph has bounded treewidth. This implies new upper bounds on extension…
Many NP-complete constraint satisfaction problems appear to undergo a "phase transition'' from solubility to insolubility when the constraint density passes through a critical threshold. In all such cases it is easy to derive upper bounds…
We consider the problem of approximately solving constraint satisfaction problems with arity $k > 2$ ($k$-CSPs) on instances satisfying certain expansion properties, when viewed as hypergraphs. Random instances of $k$-CSPs, which are also…
Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…
In the last two decades the study of random instances of constraint satisfaction problems (CSPs) has flourished across several disciplines, including computer science, mathematics and physics. The diversity of the developed methods, on the…
We initiate a systematic study of the computational complexity of the Constraint Satisfaction Problem (CSP) over finite structures that may contain both relations and operations. We show the close connection between this problem and a…
Recent results show that a constraint satisfaction problem (CSP) defined over rational numbers with their natural ordering has a solution if and only if it has a definable solution. The proof uses advanced results from topology and modern…
We study a model of constraint satisfaction problems geared towards instances with few variables but with domain of unbounded size (udCSP). Our model is inspired by recent work on FPT algorithms for MinCSP where frequently both upper and…
We show that for any odd $k$ and any instance of the Max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a $\frac{1}{2} + \Omega(1/\sqrt{D})$ fraction of constraints, where…
We prove that the property of containing a $k$-regular subgraph in the random graph model $G(n,p)$ has a sharp threshold for $k\ge3$. We also show how to use similar methods to obtain an easy prove for the (known fact of) sharpness of…
We study constraint satisfaction problems on the so-called 'planted' random ensemble. We show that for a certain class of problems, e.g. graph coloring, many of the properties of the usual random ensemble are quantitatively identical in the…
We introduce a natural generalization of the Erd\H{o}s-R\'enyi random graph model in which random instances of a fixed motif are added independently. The binomial random motif graph $G(H,n,p)$ is the random (multi)graph obtained by adding…
Survey Propagation is an algorithm designed for solving typical instances of random constraint satisfiability problems. It has been successfully tested on random 3-SAT and random $G(n,\frac{c}{n})$ graph 3-coloring, in the hard region of…
We study the complexity of constraint satisfaction problems for templates $\Gamma$ that are first-order definable in $(\Bbb Z; succ)$, the integers with the successor relation. Assuming a widely believed conjecture from finite domain…
In the constraint satisfaction problem (CSP) corresponding to a constraint language (i.e., a set of relations) $\Gamma$, the goal is to find an assignment of values to variables so that a given set of constraints specified by relations from…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
We study the phase diagram and the algorithmic hardness of the random `locked' constraint satisfaction problems, and compare them to the commonly studied 'non-locked' problems like satisfiability of boolean formulas or graph coloring. The…
We study the connection between the order of phase transitions in combinatorial problems and the complexity of decision algorithms for such problems. We rigorously show that, for a class of random constraint satisfaction problems, a limited…
There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such…