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 the parameterised counting constraint satisfaction problem: given a set of constraints over a set of variables and a positive integer $k$, how many ways are there to assign $k$ variables to 1 (and the others to 0)…
We introduce and study the random "locked" constraint satisfaction problems. When increasing the density of constraints, they display a broad "clustered" phase in which the space of solutions is divided into many isolated points. While the…
The XOR-satisfiability (XORSAT) problem requires finding an assignment of $n$ Boolean variables that satisfy $m$ exclusive OR (XOR) clauses, whereby each clause constrains a subset of the variables. We consider random XORSAT instances,…
The constraint satisfaction problem (CSP) is a general problem central to computer science and artificial intelligence. Although the CSP is NP-hard in general, considerable effort has been spent on identifying tractable subclasses. The main…
Using methods and ideas from statistical mechanics, we propose a simple method for obtaining rigorous upper bounds for satisfiability transition in random boolean expressions composed of N variables and M clauses with K variables per…
We study a simple and exactly solvable model for the generation of random satisfiability problems. These consist of $\gamma N$ random boolean constraints which are to be satisfied simultaneously by $N$ logical variables. In…
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…
The complexity of the graph isomorphism problem for trapezoid graphs has been open over a decade. This paper shows that the problem is GI-complete. More precisely, we show that the graph isomorphism problem is GI-complete for comparability…
In recent years, much attention has been placed on the complexity of graph homomorphism problems when the input is restricted to ${\mathbb P}_k$-free and ${\mathbb P}_k$-subgraph-free graphs. We consider the directed version of this…
Many constraint satisfaction problems involve synthesizing subgraphs that satisfy certain reachability constraints. This paper presents programs in Picat for four problems selected from the recent LP/CP programming competitions. The…
The quantified constraint satisfaction problem (QCSP) is a powerful framework for modelling computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…
CSP sparsification, introduced by Kogan and Krauthgamer (ITCS 2015), considers the following question: how much can an instance of a constraint satisfaction problem be sparsified (by retaining a reweighted subset of the constraints) while…
For a fixed graph $H$ and for arbitrarily large host graphs $G$, the number of homomorphisms from $H$ to $G$ and the number of subgraphs isomorphic to $H$ contained in $G$ have been extensively studied in extremal graph theory and graph…
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…
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…
We show NP-completeness for several planar variants of the monotone satisfiability problem with bounded variable appearances. With one exception the presented variants have an associated bipartite graph where the vertex degree is bounded by…
A counting constraint satisfaction problem (#CSP) asks for the number of ways to satisfy a given list of constraints, drawn from a fixed constraint language \Gamma. We study how hard it is to evaluate this number approximately. There is an…
We investigate the Constraint Satisfaction Problem (CSP) over templates with a group structure, and algorithms solving CSP that are equivariant, i.e. invariant under a natural group action induced by a template. Our main result is a method…