Related papers: Simplest random K-satisfiability problem
We investigate the complexity of solving stable or perturbation-resilient instances of $k$-Means and $k$-Median clustering in fixed dimension Euclidean metrics (more generally doubling metrics). The notion of stable (perturbation resilient)…
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…
We consider the problem of computing the satisfaction probability of a formula for stochastic models with parametric uncertainty. We show that this satisfaction probability is a smooth function of the model parameters. This enables us to…
A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent…
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…
We study the binary perceptron, a random constraint satisfaction problem that asks to find a Boolean vector in the intersection of independently chosen random halfspaces. A striking feature of this model is that at every positive constraint…
Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\geq 8$. In this phase the solutions are grouped into clusters which are far away from each other. The results are in…
Maximum satisfiability is a canonical NP-hard optimization problem that appears empirically hard for random instances. Let us say that a Conjunctive normal form (CNF) formula consisting of $k$-clauses is $p$-satisfiable if there exists a…
We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary…
The quantum statistics mechanism is very powerful for investigating the equilibrium states and the phase transitions in complex spin disorder systems. The spin disorder systems act as an interdisciplinary platform for solving the optimum…
The calculation of ground-state energies of physical systems can be formalised as the k-local Hamiltonian problem, which is the natural quantum analogue of classical constraint satisfaction problems. One way of making the problem more…
The Boolean Satisfiability Problem is perhaps one of the most well-known problems in theoretical computer science. On the one hand, it is proven to be NP-complete, which means that it is generally considered hard to solve. On the other…
In this paper we propose a random CSP model, called Model GB, which is a natural generalization of standard Model B. It is proved that Model GB in which each constraint is easy to satisfy exhibits non-trivial behaviour (not trivially…
We consider stability and uniqueness in real phase retrieval problems over general input sets. Specifically, we assume the data consists of noisy quadratic measurements of an unknown input x in R^n that lies in a general set T and study…
We review the connection between statistical mechanics and the analysis of random optimization problems, with particular emphasis on the random k-SAT problem. We discuss and characterize the different phase transitions that are met in these…
We study the random K-satisfiability problem using a partition function where each solution is reweighted according to the number of variables that satisfy every clause. We apply belief propagation and the related cavity method to the…
The subspace approximation problem Subspace($k$,$p$) asks for a $k$-dimensional linear subspace that fits a given set of points optimally, where the error for fitting is a generalization of the least squares fit and uses the $\ell_{p}$ norm…
Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning…
Random constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark instances for algorithms and they have been harnessed in probabilistic constructions of…
Two contrasting algorithmic paradigms for constraint satisfaction problems are successive local explorations of neighboring configurations versus producing new configurations using global information about the problem (e.g. approximating…