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Constraint Satisfaction Problem (CSP) is a fundamental algorithmic problem that appears in many areas of Computer Science. It can be equivalently stated as computing a homomorphism $\mbox{$\bR \rightarrow \bGamma$}$ between two relational…

Computational Complexity · Computer Science 2015-10-27 Vladimir Kolmogorov , Michal Rolinek , Rustem Takhanov

The local behavior of typical solutions of random constraint satisfaction problems (CSP) describes many important phenomena including clustering thresholds, decay of correlations, and the behavior of message passing algorithms. When the…

Probability · Mathematics 2025-02-25 Allan Sly , Youngtak Sohn

For several models of random constraint satisfaction problems, it was conjectured by physicists and later proved that a sharp satisfiability transition occurs. For random $k$-SAT and related models it happens at clause density $\alpha$…

Probability · Mathematics 2019-05-16 Zsolt Bartha , Nike Sun , Yumeng Zhang

In this paper we study the complexity of counting Constraint Satisfaction Problems (CSPs) of the form #CSP($\mathcal{C}$,-), in which the goal is, given a relational structure $\mathbf{A}$ from a class $\mathcal{C}$ of structures and an…

Computational Complexity · Computer Science 2020-05-15 Andrei A. Bulatov , Stanislav Zivny

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…

Combinatorics · Mathematics 2025-07-02 Konstantinos Panagiotou , Matija Pasch

For a constraint satisfaction problem (CSP), a robust satisfaction algorithm is one that outputs an assignment satisfying most of the constraints on instances that are near-satisfiable. It is known that the CSPs that admit efficient robust…

Data Structures and Algorithms · Computer Science 2025-09-09 Joshua Brakensiek , Venkatesan Guruswami , Sai Sandeep

The constraint satisfaction problem asks to decide if a set of constraints over a relational structure $\mathcal{A}$ is satisfiable (CSP$(\mathcal{A})$). We consider CSP$(\mathcal{A} \cup \mathcal{B})$ where $\mathcal{A}$ is a structure and…

Computational Complexity · Computer Science 2024-08-28 Peter Jonsson , Victor Lagerkvist , George Osipov

In this paper, we try to further demonstrate that the models of random CSP instances proposed by [Xu and Li, 2000; 2003] are of theoretical and practical interest. Indeed, these models, called RB and RD, present several nice features.…

Artificial Intelligence · Computer Science 2016-08-31 Ke Xu , Frederic Boussemart , Fred Hemery , Christophe Lecoutre

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…

Statistical Mechanics · Physics 2009-06-13 Florent Krzakala , Lenka Zdeborová

The Constraint Satisfaction Problem (CSP) is ubiquitous in various areas of mathematics and computer science. Many of its variations have been studied including the Counting CSP, where the goal is to find the number of solutions to a CSP…

Computational Complexity · Computer Science 2025-01-24 Amirhossein Kazeminia , Andrei A. Bulatov

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…

Disordered Systems and Neural Networks · Physics 2008-12-09 Lenka Zdeborová , Marc Mézard

We study the entropy landscape of solutions for the bicoloring problem in random graphs, a representative difficult constraint satisfaction problem. Our goal is to classify which type of clusters of solutions are addressed by different…

Statistical Mechanics · Physics 2009-11-13 L. Dall'Asta , A. Ramezanpour , R. Zecchina

Constraint satisfaction problems (CSPs) for first-order reducts of finitely bounded homogeneous structures form a large class of computational problems that might exhibit a complexity dichotomy, P versus NP-complete. A powerful method to…

Logic · Mathematics 2024-05-13 Manuel Bodirsky , Bertalan Bodor

Constraint Satisfaction Problems (CSPs) lie at the heart of complexity theory and find application in a plethora of prominent tasks ranging from cryptography to genetics. Classical approaches use Hopfield networks to find approximate…

Disordered Systems and Neural Networks · Physics 2025-12-24 Niklas Foos , Bastian Epping , Jannik Grundler , Alexandru Ciobanu , Ajainderpal Singh , Tim Bode , Moritz Helias , David Dahmen

Constraint Satisfaction Problems (CSPs) typically have many solutions that satisfy all constraints. Often though, some solutions are preferred over others, that is, some solutions dominate other solutions. We present solution dominance as a…

Artificial Intelligence · Computer Science 2018-12-24 Tias Guns , Peter J. Stuckey , Guido Tack

We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…

Discrete Mathematics · Computer Science 2012-02-06 Harold Connamacher , Michael Molloy

Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all…

Artificial Intelligence · Computer Science 2013-03-25 Thomas Schiex

We study random constraint satisfaction problems (CSPs) in the unsatisfiable regime. We relate the structure of near-optimal solutions for any Max-CSP to that for an associated spin glass on the hypercube, using the Guerra-Toninelli…

Discrete Mathematics · Computer Science 2023-03-30 Chris Jones , Kunal Marwaha , Juspreet Singh Sandhu , Jonathan Shi

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…

Computational Complexity · Computer Science 2007-05-23 Ke Xu , Wei Li

The best current estimates of the thresholds for the existence of solutions in random constraint satisfaction problems ('CSPs') mostly derive from the first and the second moment method. Yet apart from a very few exceptional cases these…

Discrete Mathematics · Computer Science 2017-11-17 Amin Coja-Oghlan , Konstantinos Panagiotou