Related papers: Sharp thresholds for constraint satisfaction probl…
This is a review paper, summarizing without proofs recent results by the authors on the property of strong metric subregularity (SMSR) in optimization. It presents sufficient conditions for SMSR of the optimality mapping associated with a…
We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used;…
For a large number of random constraint satisfaction problems, such as random k-SAT and random graph and hypergraph coloring, there are very good estimates of the largest constraint density for which solutions exist. Yet, all known…
The $H$-Coloring problem is a well-known generalization of the classical NP-complete problem $k$-Coloring where the task is to determine whether an input graph admits a homomorphism to the template graph $H$. This problem has been the…
We study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied simultaneously. In standard…
Satisfiability is considered the canonical NP-complete problem and is used as a starting point for hardness reductions in theory, while in practice heuristic SAT solving algorithms can solve large-scale industrial SAT instances very…
We prove that $(1+o(1))\sqrt{e/n}$ is the sharp threshold for the appearance of the square of a Hamilton cycle in $G(n,p)$, confirming the conjecture of Kahn, Narayanan, and Park. We also find the exact asymptotics of the threshold for the…
We determine the exact freezing threshold, r^f, for a family of models of random boolean constraint satisfaction problems, including NAE-SAT and hypergraph 2-colouring, when the constraint size is sufficiently large. If the…
We completely classify the computational complexity of the list H-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph H the problem is either NP-complete, NL-complete, L-complete or is…
We will present a new method, which enables us to find threshold functions for many properties in random intersection graphs. This method will be used to establish sharp threshold functions in random intersection graphs for k-connectivity,…
This survey concerns regular graphs that are extremal with respect to the number of independent sets, and more generally, graph homomorphisms. More precisely, in the family of of $d$-regular graphs, which graph $G$ maximizes/minimizes the…
In this paper we study two natural models of \textit{random temporal} graphs. In the first, the \textit{continuous} model, each edge $e$ is assigned $l_e$ labels, each drawn uniformly at random from $(0,1]$, where the numbers $l_e$ are…
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
This paper studies a class of probabilistic models on graphs, where edge variables depend on incident node variables through a fixed probability kernel. The class includes planted con- straint satisfaction problems (CSPs), as well as more…
Using the cavity equations of \cite{mezard:parisi:zecchina:02,mezard:zecchina:02}, we derive the various threshold values for the number of clauses per variable of the random $K$-satisfiability problem, generalizing the previous results to…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
The interplay of minimum degree conditions and structural properties of large graphs with forbidden subgraphs is a central topic in extremal graph theory. For a given graph $F$ we define the homomorphism threshold as the infimum over all…
Inhomogeneous random graphs are fundamental models for real-world networks, where prescribed degrees are imposed as soft constraints. A common assumption in such models is that the degree distribution follows a power-law, capturing the…
In this paper we show that $e/n$ is the sharp threshold for the existence of tight Hamilton cycles in random $k$-uniform hypergraphs, for all $k\ge 4$. When $k=3$ we show that $1/n$ is an asymptotic threshold. We also determine thresholds…
The semiring-based constraint satisfaction problems (semiring CSPs), proposed by Bistarelli, Montanari and Rossi \cite{BMR97}, is a very general framework of soft constraints. In this paper we propose an abstraction scheme for soft…