Constraint satisfaction problems (CSPs) models many important intractable NP-hard problems such as propositional satisfiability problem (SAT). Algorithms with non-trivial upper bounds on running time for restricted SAT with bounded clause length k (k-SAT) can be classified into three styles: DPLL-like, PPSZ-like and Local Search, with local search algorithms having already been generalized to CSP with bounded constraint arity k (k-CSP). We generalize a DPLL-like algorithm in its simplest form and a PPSZ-like algorithm from k-SAT to k-CSP. As far as we know, this is the first attempt to use PPSZ-like strategy to solve k-CSP, and before little work has been focused on the DPLL-like or PPSZ-like strategies for k-CSP.
TU Berlin（柏林工业大学）；UNSW Sydney（新南威尔士大学悉尼分校）；Germany and Australia（德国和澳大利亚（注：此处根据上下文理解为作者所属机构所在国家/地区，非独立机构名称，严格按要求仅提取明确机构名，故原文本中该部分不单独作为机构提取））
In 2000, I published a relatively comprehensive study of mappings between propositional satisfiability (SAT) and constraint satisfaction problems (CSPs) [Wal00]. I analysed four different mappings of SAT problems into CSPs, and two of CSPs into SAT problems. For each mapping, I compared the impact of achieving arc-consistency on the CSP with unit propagation on the corresponding SAT problems, and lifted these results to CSP algorithms that maintain (some level of ) arc-consistency during search like FC and MAC, and to the Davis- Putnam procedure (which performs unit propagation at each search …
CNRS（法国国家科学研究中心）；University of Toulouse（图卢兹大学）；INP Toulouse（图卢兹国立理工学院）
Given a fixed constraint language $Γ$, the conservative CSP over $Γ$ (denoted by c-CSP($Γ$)) is a variant of CSP($Γ$) where the domain of each variable can be restricted arbitrarily. A dichotomy is known for conservative CSP: for every fixed language $Γ$, c-CSP($Γ$) is either in P or NP-complete. However, the characterization of conservatively tractable languages is of algebraic nature and the naive recognition algorithm is super-exponential in the domain size. The main contribution of this paper is a polynomial-time algorithm that, given a constraint language $Γ$ as input, decides if c-CSP($Γ…
This paper describes an extension to the constraint satisfaction problem (CSP) called MUSE CSP (MUltiply SEgmented Constraint Satisfaction Problem). This extension is especially useful for those problems which segment into multiple sets of partially shared variables. Such problems arise naturally in signal processing applications including computer vision, speech processing, and handwriting recognition. For these applications, it is often difficult to segment the data in only one way given the low-level information utilized by the segmentation algorithms. MUSE CSP can be used to compactly repr…
Insight Centre for Data Analytics（Insight数据分析中心）；University College Cork（科克大学学院）
In recent years, portfolio approaches to solving SAT problems and CSPs have become increasingly common. There are also a number of different encodings for representing CSPs as SAT instances. In this paper, we leverage advances in both SAT and CSP solving to present a novel hierarchical portfolio-based approach to CSP solving, which we call Proteus, that does not rely purely on CSP solvers. Instead, it may decide that it is best to encode a CSP problem instance into SAT, selecting an appropriate encoding and a corresponding SAT solver. Our experimental evaluation used an instance of Proteus tha…
Combinatorial problems stated as Constraint Satisfaction Problems (CSP) are examined. It is shown by example that any algorithm designed for the original CSP, and involving the AllDifferent constraint, has at least the same level of efficacy when simultaneously applied to both the original and its complementary problem. The 1-to-1 mapping employed to transform a CSP to its complementary problem, which is also a CSP, is introduced. This "Dual CSP" method and its application are outlined. The analysis of several random problem instances demonstrate the benefits of this method for variable domain…
University of Lethbridge（莱斯布里奇大学）；InBridge Inc（英桥公司）
We study the design of stochastic local search methods to prove unsatisfiability of a constraint satisfaction problem (CSP). For a binary CSP, such methods have been designed using the microstructure of the CSP. Here, we develop a method to decompose the microstructure into graph tensors. We show how to use the tensor decomposition to compute a proof of unsatisfiability efficiently and in parallel. We also offer substantial empirical evidence that our approach improves the praxis. For instance, one decomposition yields proofs of unsatisfiability in half the time without sacrificing the quality…
Structural decomposition methods, such as generalized hypertree decompositions, have been successfully used for solving constraint satisfaction problems (CSPs). As decompositions can be reused to solve CSPs with the same constraint scopes, investing resources in computing good decompositions is beneficial, even though the computation itself is hard. Unfortunately, current methods need to compute a completely new decomposition even if the scopes change only slightly. In this paper, we make the first steps toward solving the problem of updating the decomposition of a CSP $P$ so that it becomes a…
INRIA（法国国家信息与自动化研究所）；University of Bologna（博洛尼亚大学）
Recent research in areas such as SAT solving and Integer Linear Programming has shown that the performances of a single arbitrarily efficient solver can be significantly outperformed by a portfolio of possibly slower on-average solvers. We report an empirical evaluation and comparison of portfolio approaches applied to Constraint Satisfaction Problems (CSPs). We compared models developed on top of off-the-shelf machine learning algorithms with respect to approaches used in the SAT field and adapted for CSPs, considering different portfolio sizes and using as evaluation metrics the number of so…
We present ULSA, a novel stochastic local search algorithm for random binary constraint satisfaction problems (CSP). ULSA is many times faster than the prior state of the art on a widely-studied suite of random CSP benchmarks. Unlike the best previous methods for these benchmarks, ULSA is a simple unweighted method that does not require dynamic adaptation of weights or penalties. ULSA obtains new record best solutions satisfying 99 of 100 variables in the challenging frb100-40 benchmark instance.
Backtracking is a basic strategy to solve constraint satisfaction problems (CSPs). A satisfiable CSP instance is backtrack-free if a solution can be found without encountering any dead-end during a backtracking search, implying that the instance is easy to solve. We prove an exact phase transition of backtrack-free search in some random CSPs, namely in Model RB and in Model RD. This is the first time an exact phase transition of backtrack-free search can be identified on some random CSPs. Our technical results also have interesting implications on the power of greedy algorithms, on the width o…
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 formal framework to reason about such settings. We define Constraint Dominance Problems (CDPs) as CSPs with a dominance relation, that is, a preorder over the solutions of the CSP. This framework captures many well-known variants of constraint satisfaction, including optimization, multi-objective optimization, Max-CSP, minimal models, minimum correction sub…
We introduce an efficient message passing scheme for solving Constraint Satisfaction Problems (CSPs), which uses stochastic perturbation of Belief Propagation (BP) and Survey Propagation (SP) messages to bypass decimation and directly produce a single satisfying assignment. Our first CSP solver, called Perturbed Blief Propagation, smoothly interpolates two well-known inference procedures; it starts as BP and ends as a Gibbs sampler, which produces a single sample from the set of solutions. Moreover we apply a similar perturbation scheme to SP to produce another CSP solver, Perturbed Survey Pro…
CRIL - CNRS, University of Artois, France（法国阿尔图瓦大学，CRIL - CNRS）
In this paper, we propose an extension of our Mining for SAT framework to Constraint satisfaction Problem (CSP). We consider n-ary extensional constraints (table constraints). Our approach aims to reduce the size of the CSP by exploiting the structure of the constraints graph and of its associated microstructure. More precisely, we apply itemset mining techniques to search for closed frequent itemsets on these two representation. Using Tseitin extension, we rewrite the whole CSP to another compressed CSP equivalent with respect to satisfiability. Our approach contrast with previous proposed ap…
Universidad del País Vasco（巴斯克大学）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯克，巴斯克科学基金会）
The constraint satisfaction problem (CSP) on a relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is a assignment to the variables satisfying all of the constraints; the surjective CSP is the variant where one decides the existence of a surjective satisfying assignment onto the universe of B. We present an algebraic condition on the polymorphism clone of B and prove that it is sufficient for the hardness of the surjective CSP on a finite structure B, in the sense that this problem admits a reduction from a certain …
University of Oxford（牛津大学）；Royal Holloway, University of London（伦敦大学皇家霍洛威学院）；IRIT, University of Toulouse III（图卢兹第三大学IRIT研究所）
Singleton arc consistency is an important type of local consistency which has been recently shown to solve all constraint satisfaction problems (CSPs) over constraint languages of bounded width. We aim to characterise all classes of CSPs defined by a forbidden pattern that are solved by singleton arc consistency and closed under removing constraints. We identify five new patterns whose absence ensures solvability by singleton arc consistency, four of which are provably maximal and three of which generalise 2-SAT. Combined with simple counter-examples for other patterns, we make significant pro…
The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of Constraint Satisfaction Problems (#CSP). We consider the random model, i.e. RB model. We prove that phase transition of #CSP does exist as the number of variables approaches infinity and the critical values where phase transitions occur are precisely located. Preliminary experimental results also show that the critical point coincides with the theoretical derivati…
University of the Basque Country (UPV/EHU)（巴斯克大学）；IKERBASQUE, Basque Foundation for Science（巴斯克科学基金会）；Concordia University（康考迪亚大学）
The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of the CSP is as the problem of deciding, given a pair (G,H) of relational structures, whether or not there is a homomorphism from the first structure to the second structure. The CSP is in general NP-hard; a common way to restrict this problem is to fix the second structure H, so that each structure H gives rise to a problem CSP(H). The problem family CSP(H) has…
Hamilton Institute, National University of Ireland Maynooth（爱尔兰国立大学梅努斯分校汉密尔顿研究所）；University of Toulouse（图卢兹大学）
We show that several important resource allocation problems in wireless networks fit within the common framework of Constraint Satisfaction Problems (CSPs). Inspired by the requirements of these applications, where variables are located at distinct network devices that may not be able to communicate but may interfere, we define natural criteria that a CSP solver must possess in order to be practical. We term these algorithms decentralized CSP solvers. The best known CSP solvers were designed for centralized problems and do not meet these criteria. We introduce a stochastic decentralized CSP so…
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 satisfiable or unsatisfiable) as the number of variables approaches infinity. A detailed analysis to obtain an asymptotic estimate (good to 1+o(1)) of the average number of nodes in a search tree used by the backtracking algorithm on Model GB is also presented. It is shown that the average number of nodes required for finding all solutions or proving that no solut…
The constraint satisfaction problem (CSP) and its quantified extensions, whether without (QCSP) or with disjunction (QCSP_or), correspond naturally to the model checking problem for three increasingly stronger fragments of positive first-order logic. Their complexity is often studied when parameterised by a fixed model, the so-called template. It is a natural question to ask when two templates are equivalent, or more generally when one "contain" another, in the sense that a satisfied instance of the first will be necessarily satisfied in the second. One can also ask for a smallest possible equ…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed combinations of values, or implicitly, by special-purpose algorithms provided by a solver. Such implicitly represented constraints, known as global constraints, are widely used; indeed, they are one of the key reasons for the success of constraint programming in solving real-world problems. In recent years, a variety of restrictions on the structure of CSP inst…
Université Paris Diderot – Paris 7（巴黎第七大学（巴黎狄德罗大学））；Université Paris 7（巴黎第七大学）；CNRS（法国国家科学研究中心）；Université Paris 6（巴黎第六大学）；Albert-Ludwigs-Universität Freiburg（阿尔伯特-路德维希-弗莱堡大学）；ENS Lyon（里昂高等师范学院）；INRIA（法国国家信息与自动化研究所）；ENS Cachan（卡尚高等师范学院）；Université Pompeu Fabra（庞培法布拉大学）；Université de Linköping（林雪平大学）
A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values to the variables. Depending on the type of constraints that we allow in the input, a CSP might be tractable, or computationally hard. In recent years, general criteria have been discovered that imply that a CSP is polynomial-time tractable, or that it is NP-hard. Finite-domain CSPs have become a major common research focus of graph theory, artificial intell…
University of Manouba（马努巴大学）；National School of Computer Science（国立计算机科学学院）；University of Strasbourg（斯特拉斯堡大学）；Taibah University（塔伊巴大学）；College of Computer Science and Engineering（计算机科学与工程学院）
Constraint satisfaction problem (CSP) has been actively used for modeling and solving a wide range of complex real-world problems. However, it has been proven that developing efficient methods for solving CSP, especially for large problems, is very difficult and challenging. Existing complete methods for problem-solving are in most cases unsuitable. Therefore, proposing hybrid CSP-based methods for problem-solving has been of increasing interest in the last decades. This paper aims at proposing a novel approach that combines incomplete and complete CSP methods for problem-solving. The proposed…
This paper reviews the connections between Graphplan's planning-graph and the dynamic constraint satisfaction problem and motivates the need for adapting CSP search techniques to the Graphplan algorithm. It then describes how explanation based learning, dependency directed backtracking, dynamic variable ordering, forward checking, sticky values and random-restart search strategies can be adapted to Graphplan. Empirical results are provided to demonstrate that these augmentations improve Graphplan's performance significantly (up to 1000x speedups) on several benchmark problems. Special attentio…
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 given constraints between these variables. However, for many real tasks such as job-shop scheduling, time-table scheduling, design?, all these constraints have not the same significance and have not to be necessarily satisfied. A first distinction can be made between hard constraints, which every solution should satisfy and soft constraints, whose satisfactio…
Faculty of Mathematics, University of Belgrade（贝尔格莱德大学数学学院）
Many different approaches for solving Constraint Satisfaction Problems (CSPs) and related Constraint Optimization Problems (COPs) exist. However, there is no single solver (nor approach) that performs well on all classes of problems and many portfolio approaches for selecting a suitable solver based on simple syntactic features of the input CSP instance have been developed. In this paper we first present a simple portfolio method for CSP based on k-nearest neighbors method. Then, we propose a new way of using portfolio systems --- training them shortly in the exploitation time, specifically fo…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed combinations of values, or implicitly, by special-purpose algorithms provided by a solver. Such implicitly represented constraints, known as global constraints, are widely used; indeed, they are one of the key reasons for the success of constraint programming in solving real-world problems. In recent years, a variety of restrictions on the structure of CSP inst…
Brandenburg University of Technology Cottbus-Senftenberg（科特布斯-森夫滕贝格勃兰登堡工业大学）
This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of fails in the resolution process, to improve the inferences made during search by the constraint solver by strengthening constraint propagation, and to maintain the level of propagation while reducing the cost of propagating the constraints. Our experimental results show improvements in terms of the resolution speed compared to the original CSPs and a compet…
Shandong University（山东大学）；Singapore Institute of Manufacturing Technology（新加坡制造技术研究院）；Nanyang Technological University（南洋理工大学）；Southwest Jiaotong University（西南交通大学）
Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP). The efficiency of backtracking search depends greatly on the variable ordering heuristics. Currently, the most commonly used heuristics are hand-crafted based on expert knowledge. In this paper, we propose a deep reinforcement learning based approach to automatically discover new variable ordering heuristics that are better adapted for a given class of CSP instances. We show that directly optimizing the search cost is hard for bootstrapping, and propose to optimize the expected cost of reaching a …
Self-Supervised Transformers as Iterative Solution Improvers for Constraint Satisfaction
University of Toronto（多伦多大学）；Vector Institute for Artificial Intelligence（向量人工智能研究所）；Scale AI Research Chair in Data-Driven Algorithms for Modern Supply Chains（数据驱动算法现代供应链研究席位）
We show how one can use certain deterministic algorithms for higher-value constraint satisfaction problems (CSPs) to speed up deterministic local search for 3-SAT. This way, we improve the deterministic worst-case running time for 3-SAT to O(1.439^n).
We study the complexity of approximate counting Constraint Satisfaction Problems (#CSPs) in a bounded degree setting. Specifically, given a Boolean constraint language $Γ$ and a degree bound $Δ$, we study the complexity of #CSP$_Δ(Γ)$, which is the problem of counting satisfying assignments to CSP instances with constraints from $Γ$ and whose variables can appear at most $Δ$ times. Our main result shows that: (i) if every function in $Γ$ is affine, then #CSP$_Δ(Γ)$ is in FP for all $Δ$, (ii) otherwise, if every function in $Γ$ is in a class called IM$_2$, then for all sufficiently large $Δ$, #…
Random constraint satisfaction problems (CSPs) such as random $3$-SAT are conjectured to be computationally intractable. The average case hardness of random $3$-SAT and other CSPs has broad and far-reaching implications on problems in approximation, learning theory and cryptography. In this work, we show subexponential lower bounds on the size of linear programming relaxations for refuting random instances of constraint satisfaction problems. Formally, suppose $P : \{0,1\}^k \to \{0,1\}$ is a predicate that supports a $t-1$-wise uniform distribution on its satisfying assignments. Consider the …
An instance of the Constraint Satisfaction Problem (CSP) is given by a family of constraints on overlapping sets of variables, and the goal is to assign values from a fixed domain to the variables so that all constraints are satisfied. In the optimization version, the goal is to maximize the number of satisfied constraints. An approximation algorithm for CSP is called robust if it outputs an assignment satisfying a $(1-g(\varepsilon))$-fraction of constraints on any $(1-\varepsilon)$-satisfiable instance, where the loss function $g$ is such that $g(\varepsilon)\rightarrow 0$ as $\varepsilon\ri…
In the Boolean maximum constraint satisfaction problem - Max CSP$(Γ)$ - one is given a collection of weighted applications of constraints from a finite constraint language $Γ$, over a common set of variables, and the goal is to assign Boolean values to the variables so that the total weight of satisfied constraints is maximized. There exists an elegant dichotomy theorem providing a criterion on $Γ$ for the problem to be polynomial-time solvable and stating that otherwise it becomes NP-hard. We study the NP hard cases through the lens of kernelization and provide a complete characterization of …
In the Permutation Constraint Satisfaction Problem (Permutation CSP) we are given a set of variables $V$ and a set of constraints C, in which constraints are tuples of elements of V. The goal is to find a total ordering of the variables, $π : V \rightarrow [1,...,|V|]$, which satisfies as many constraints as possible. A constraint $(v_1,v_2,...,v_k)$ is satisfied by an ordering $π$ when $π(v_1)<π(v_2)<...<π(v_k)$. An instance has arity $k$ if all the constraints involve at most $k$ elements. This problem expresses a variety of permutation problems including {\sc Feedback Arc Set} and {\sc Betw…
An active topic in the study of random constraint satisfaction problems (CSPs) is the geometry of the space of satisfying or almost satisfying assignments as the function of the density, for which a precise landscape of predictions has been made via statistical physics-based heuristics. In parallel, there has been a recent flurry of work on refuting random constraint satisfaction problems, via nailing refutation thresholds for spectral and semidefinite programming-based algorithms, and also on counting solutions to CSPs. Inspired by this, the starting point for our work is the following questi…
For a finite relational structure A, let CSP(A) denote the CSP instances whose constraint relations are taken from A. The resulting family of problems CSP(A) has been considered heavily in a variety of computational contexts. In this article, we consider this family from the perspective of property testing: given an instance of a CSP and query access to an assignment, one wants to decide whether the assignment satisfies the instance, or is far from so doing. While previous works on this scenario studied concrete templates or restricted classes of structures, this article presents comprehensive…
Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple semidefinite programming and a rounding scheme for it. In this paper, we show that similar results hold for constant-time approximation algorithms in the bounded-degree model. Specifically, we present the followings: (i) For every CSP, we construct an oracle that serves an access, in constant time, to a nearly optimal solution to a basic LP relaxation of the CSP. (…
In the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must distinguish between being able to satisfy all the strict constraints versus not being able to satisfy all the weak constraints. The most commonly cited example of a promise CSP is the approximate graph coloring problem--which has recently seen exciting progress [BKO19, WZ20] benefiting from a systematic algebraic approach to promise CSPs based on "polymorphisms," op…
An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP instances (i.e., where each constraint involves only two variables), the situation is well understood: the complexity of the problem essentially depends on the treewidth of the graph of the constraints. However, this is not the correct answer if constraints with unbounded number of variables are allowed, and in particular, for CSP instances arising from query evalu…
In a $(k,2)$-Constraint Satisfaction Problem we are given a set of arbitrary constraints on pairs of $k$-ary variables, and are asked to find an assignment of values to these variables such that all constraints are satisfied. The $(k,2)$-CSP problem generalizes problems like $k$-coloring and $k$-list-coloring. In the Unique $(k,2)$-CSP problem, we add the assumption that the input set of constraints has at most one satisfying assignment. Beigel and Eppstein gave an algorithm for $(k,2)$-CSP running in time $O\left(\left(0.4518k\right)^n\right)$ for $k>3$ and $O\left(1.356^n\right)$ for $k=3$, …
Promise CSPs are a relaxation of constraint satisfaction problems where the goal is to find an assignment satisfying a relaxed version of the constraints. Several well-known problems can be cast as promise CSPs including approximate graph coloring, discrepancy minimization, and interesting variants of satisfiability. Similar to CSPs, the tractability of promise CSPs can be tied to the structure of operations on the solution space called polymorphisms, though in the promise world these operations are much less constrained. Under the thesis that non-trivial polymorphisms govern tractability, pro…
We consider worst case time bounds for NP-complete problems including 3-SAT, 3-coloring, 3-edge-coloring, and 3-list-coloring. Our algorithms are based on a constraint satisfaction (CSP) formulation of these problems. 3-SAT is equivalent to (2,3)-CSP while the other problems above are special cases of (3,2)-CSP; there is also a natural duality transformation from (a,b)-CSP to (b,a)-CSP. We give a fast algorithm for (3,2)-CSP and use it to improve the time bounds for solving the other problems listed above. Our techniques involve a mixture of Davis-Putnam-style backtracking with more sophistica…
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 highly expanding, are well-known to be hard to approximate using known algorithmic techniques (and are widely believed to be hard to approximate in polynomial time). However, we show that this is not necessarily the case for instances where the hypergraph is a high-dimensional expander. We consider the spectral definition of high-dimensional expansion used by…
We consider worst case time bounds for NP-complete problems including 3-SAT, 3-coloring, 3-edge-coloring, and 3-list-coloring. Our algorithms are based on a constraint satisfaction (CSP) formulation of these problems; 3-SAT is equivalent to (2,3)-CSP while the other problems above are special cases of (3,2)-CSP. We give a fast algorithm for (3,2)-CSP and use it to improve the time bounds for solving the other problems listed above. Our techniques involve a mixture of Davis-Putnam-style backtracking with more sophisticated matching and network flow based ideas.
We present a unified framework on the limits of constraint satisfaction problems (CSPs) and efficient parameter testing which depends only on array exchangeability and the method of cut decomposition without recourse to the weakly regular partitions. In particular, we formulate and prove a representation theorem for compact colored $r$-uniform directed hypergraph ($r$-graph) limits, and apply this to $r$CSP limits. We investigate the sample complexity of testable $r$-graph parameters, we discuss the generalized ground state energies and demonstrate that they are efficiently testable.
In this paper we introduce "hybrid" Max 2-CSP formulas consisting of "simple clauses", namely conjunctions and disjunctions of pairs of variables, and general 2-variable clauses, which can be any integer-valued functions of pairs of boolean variables. This allows an algorithm to use both efficient reductions specific to AND and OR clauses, and other powerful reductions that require the general CSP setting. We use new reductions introduced here, and recent reductions such as "clause-learning" and "2-reductions" generalized to our setting's mixture of simple and general clauses. Parametrizing an…
The Constraint Satisfaction Problem (CSP) is a central and generic computational problem which provides a common framework for many theoretical and practical applications. A central line of research is concerned with the identification of classes of instances for which CSP can be solved in polynomial time; such classes are often called "islands of tractability." A prominent way of defining islands of tractability for CSP is to restrict the relations that may occur in the constraints to a fixed set, called a constraint language, whereas a constraint language is conservative if it contains all u…
Strong Refutation of Ordering, Phylogenetic, and Ordinary CSPs, and New Satisfiability and Refutation Thresholds for Triplet and Quartet Reconstruction
Northwestern University（西北大学）；UC Santa Cruz（加州大学圣克鲁兹分校）
