the expressive power of valued constraints hierarchies and collapses in this paper we investigate the ways in which a fixed collection of valued constraints can be combined to express other valued constraints we show that in some cases a large class of valued constraints of all possible arities can be expressed by using valued constraints over the same domain of a fixed finite arity we also show that some simple classes of valued constraints including the set of all monotonic valued constraints with finite cost values cannot be expressed by a subset of any fixed finite arity and hence form an infinite hierarchy

a fast method for solving the heat equation by layer potentials boundary integral formulations of the heat equation involve time convolutions in addition to surface potentials if m is the number of time steps and n is the number of degrees of freedom of the spatial discretization then the direct computation of a heat potential involves order n2m2 operations this article describes a fast method to compute three dimensional heat potentials which is based on chebyshev interpolation of the heat kernel in both space and time the computational complexity is order p4q2nm operations where p and q are the orders of the polynomial approximation in space and time

domain permutation reduction for constraint satisfaction problems this paper is concerned with the constraint satisfaction problem csp it is well known that the general csp is np hard however there has been significant success in discovering subproblems which are tractable polynomial time solvable one of the most effective ways to obtain a tractable subproblem has been to force all of the constraint relations to lie in some tractable language in this paper we define a new way of identifying tractable subproblems of the csp let p be an arbitrary csp instance and c be any tractable language suppose there exists for each variable of p a permutation of the domain such the resultant permuted constraint relations of p all lie in c the domain permuted instance is then an instance of a tractable class and can be solved by the polynomial time algorithm for c solutions to p can be obtained by inverting the domain permutations the question for a given class of instances and language c whether such a set of domain permutations can be found efficiently is the key to this method s tractability one of the important contributions made in this paper is the notion of a lifted constraint instance which is a powerful tool to study this question we consider the open problem of discovering domain permutations which make instances max closed we show that for bounded arity instances over a boolean domain this problem is tractable while for domain size three it is intractable even for binary instances we give a simple proof verifying the tractability of discovering domain permutations which make instances row convex we refute a published result by giving a simple proof of the intractability of discovering domain permutations which make instances even with domain size four connected row convex we demonstrate that triangulated and stable marriage instances are reducible via domain permutations to max closed instances this provides a simple explanation for arc consistency deciding these instances we verify with a simple direct proof the tractability of identification of renamable horn instances and the intractability of finding the largest renamable horn subset of clauses of an instance of sat we describe natural tractable classes which properly extend the maximal relational classes arising from tractable constraint languages we believe that domain permutation reductions have a significant chance of being useful in practical applications

on numerical cubatures of singular surface integrals in boundary element methods we present and analyze methods for the accurate and efficient evaluation of weakly cauchy and hypersingular integrals over piecewise analytic curved surfaces in 3 the class of admissible integrands includes all kernels arising in the numerical solution of elliptic boundary value problems in three dimensional domains by the boundary integral equation method the possibly not absolutely integrable kernels of boundary integral operators in local coordinates are pseudohomogeneous with analytic characteristics depending on the local geometry of the surface at the source point this rules out weighted quadrature approaches with a fixed singular weight for weakly singular integrals it is shown that duffy s triangular coordinates leadalways to a removal of the kernel singularity also asymptotic estimates of the integration error are provided as the size of the boundary element patch tends to zero these are based on the rabinowitz richter estimates in connection with an asymptotic estimate of domains of analyticity in 2 it is further shown that the modified extrapolation approach due to lyness is in the weakly singular case always applicable corresponding error and asymptotic work estimates are presented for the weakly singular as well as for cauchy and hypersingular integrals which e g arise in the study of crack problems we analyze a family of product integration rules in local polar coordinates these rules are hierarchically constructed from finite part integration formulas in radial and gaussian formulas in angular direction again we show how the rabinowitz richter estimates can be applied providing asymptotic error estimates in terms of orders of the boundary element size

the modified trapezoidal rule for line integrals although the predictor corrector curve tracing method has found a wide variety of significant applications the calculation of line integrals over implicitly defined curves seems to have been overlooked in this paper we present two modified numerical integration techniques namely the modified trapezoidal and the modified romberg rules and results of some numerical experiments for evaluating the line integral of a vector field over an implicitly defined curve moreover we give a proof of an asymptotic error expansion for a modified trapezoidal rule which is a modification of that of verlinden and cools 8

constraint relaxation may be perfect abstract networks of constraints are a simple knowledge representation method useful for describing those problems whose solution is required to satisfy several simultaneous constraints the problem of solving a network of constraints with finite domains is np complete the standard solution technique for such networks of constraints is the backtrack search but many relaxation algorithms to be applied before backtracking have been developed they transform a network in an equivalent but more explicit one the idea is to make the backtrack search have a better average time complexity in fact if the network elaborated by the backtrack algorithm is more explicit the algorithm backtracks less in this paper we describe relaxation algorithms as sequences of applications of relaxation rules moreover we define perfect relaxation algorithms as relaxation algorithms which not only return a more explicit network but also exactly solve the given network of constraints by applying every relaxation rule only once finally we characterize a family of classes of networks on which certain perfect relaxation algorithms are very efficient the exact solution of each network in a class is found in linear time

numerical evaluation of line integrals in this paper some simple methods for the calculation of line integrals over smooth curves are considered where an explicitly differential parametrization for the curve is either not available or is inconvenient to differentiate explicitly the method consists in first replacing a parametrization of the curve by a piecewise polynomial interpolant of it and then using a newton cotes formula for the integration of the resulting integral the surprising result is that the order of convergence of the resulting quadrature is higher than would be expected on the basis of interpolation theory alone indeed an interpolation polynomial of order p degree p 1 reproduces the derivatives of the parametrization function needed for line integrals only up to order p 1 but on using on each subinterval an interpolation formula of order p coupled with a newton cotes quadrature rule using p nodes the resulting integration method has the same order as would be obtained by applying only the newton cotes form

proof of a conjectured asymptotic expansion for the approximation of surface integrals georg introduced a new kind of trapezoidal rule and midpoint rule to approximate a surface integral over a curved triangular surface and conjectured the existence of an asymptotic expansion for this approximation as the subdivision of the surface gets finer the purpose of this paper is to prove the conjecture

learnability of quantified formulas we consider the following classes of quantified formulas fix a set of basic relations called a basis take conjunctions of these basic relations applied to variables and constants in arbitrary ways finally quantify existentially or universally some of the variables we introduce some conditions on the basis that guarantee efficient learnability furthermore we show that with certain restrictions on the basis the classification is complete we introduce as an intermediate tool a link between this class of quantified formulas and some well studied structures in universal algebra called clones more precisely we prove that the computational complexity of the learnability of these formulas is completely determined by a simple algebraic property of the basis of relations their clone of polymorphisms finally we use this technique to give a simpler proof of the already known dichotomy theorem over boolean domains

numerical evaluation of surface integrals in three dimensions in this paper we consider the evaluation of surface integrals over piecewise smooth surfaces in three dimensions the method consists in first replacing a parametrization for the surface and the integrand function by piecewise polynomial interpolants of them and second using a numerical integration scheme for the resulting integral the order of convergence is higher than would be expected based on the underlying interpolation theory

hard constraint satisfaction problems have hard gaps at location 1 an instance of the maximum constraint satisfaction problem max csp is a finite collection of constraints on a set of variables and the goal is to assign values to the variables that maximises the number of satisfied constraints max csp captures many well known problems such as maxk sat and max cut and is consequently np hard thus it is natural to study how restrictions on the allowed constraint types or constraint language affect the complexity and approximability of max csp the pcp theorem is equivalent to the existence of a constraint language for which max csp has a hard gap at location 1 i e it is np hard to distinguish between satisfiable instances and instances where at most some constant fraction of the constraints are satisfiable all constraint languages for which the csp problem i e the problem of deciding whether all constraints can be satisfied is currently known to be np hard have a certain algebraic property we prove that any constraint language with this algebraic property makes max csp have a hard gap at location 1 which in particular implies that such problems cannot have a ptas unless p np we then apply this result to max csp restricted to a single constraint type this class of problems contains for instance max cut and max dicut assuming p np we show that such problems do not admit ptas except in some trivial cases our results hold even if the number of occurrences of each variable is bounded by a constant finally we give some applications of our results

nonparametric independence screening in sparse ultra high dimensional varying coefficient models the varying coefficient model is an important class of nonparametric statistical model which allows us to examine how the effects of covariates vary with exposure variables when the number of covariates is large the issue of variable selection arises in this article we propose and investigate marginal nonparametric screening methods to screen variables in sparse ultra high dimensional varying coefficient models the proposed nonparametric independence screening nis selects variables by ranking a measure of the nonparametric marginal contributions of each covariate given the exposure variable the sure independent screening property is established under some mild technical conditions when the dimensionality is of nonpolynomial order and the dimensionality reduction of nis is quantified to enhance the practical utility and finite sample performance two data driven iterative nis inis methods are proposed for selecting thresholding parameters and variables conditional permutation and greedy metho

on the minimality and global consistency of row convex constraint networks constraint networks have been shown to be useful in formulating such diverse problems as scene labeling natural language parsing and temporal reasoning given a constraint network we often wish to i find a solution that satisfies the constraints and ii find the corresponding minimal network where the constraints are as explicit as possible both tasks are known to be np complete in the general case task 1 is usually solved using a backtracking algorithm and task ii is often solved only approximately by enforcing various levels of local consistency in this paper we identify a property of binary constraint called row convexity and show its usefulness in deciding when a form of local consistency called path consistency is sufficient to guarantee that a network is both minimal and globally consistent globally consistent networks have the property that a solution can be found without backtracking we show that one can test for the row convexity property efficiently and we show by examining applications of constraint networks discussed in the literature that our results are useful in practice thus we identify a class of binary constraint networks for which we can solve both tasks i and ii efficiently finally we generalize the results for binary constraint networks to networks with nonbinary constraints

combinatorial problems raised from 2 semilattices abstract the constraint satisfaction problem csp provides a general framework for many combinatorial problems in a a bulatov a a krokhin p g jeavons classifying the complexity of constraints using finite algebras siam j comput 34 3 2005 720 742 p g jeavons on the algebraic structure of combinatorial problems theoret comput sci 200 1998 185 204 and then in a a bulatov p g jeavons algebraic structures in combinatorial problems technical report math al 4 2001 technische universitat dresden dresden germany 2001 a new approach to the study of the csp has been developed which uses properties of universal algebras assigned to certain subclasses of the csp such that the time complexity and other properties of subclasses can be derived from the properties of the assigned algebras in this paper we briefly survey this approach and then prove that problem classes corresponding to finite 2 semilattices that is groupoids satisfying the identities x x x x y y x x x y x x y can be solved in polynomial time making use of this result we classify finite conservative groupoids and 4 element algebras with minimal clone of term operations with respect to the complexity of the corresponding csp class

classifying the complexity of constraints using finite algebras 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 here we show that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and we explore how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra hence we completely translate the problem of classifying the complexity of restricted constraint satisfaction problems into the language of universal algebra we introduce a notion of tractable algebra and investigate how the tractability of an algebra relates to the tractability of the smaller algebras which may be derived from it including its subalgebras and homomorphic images this allows us to reduce significantly the types of algebras which need to be classified using our results we also show that if the decision problem associated with a given collection of constraint types can be solved efficiently then so can the corresponding search problem we then classify all finite strictly simple surjective algebras with respect to tractability obtaining a dichotomy theorem which generalizes schaefer s dichotomy for the generalized satisfiability problem finally we suggest a possible general algebraic criterion for distinguishing the tractable and intractable cases of the constraint satisfaction problem

characterising tractable constraints abstract finding solutions to a binary constraint satisfaction problem is known to be an np complete problem in general but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted this paper considers restricted sets of constraints which are closed under permutation of the labels we identify a set of constraints which gives rise to a class of tractable problems and give polynomial time algorithms for solving such problems and for finding the equivalent minimal network we also prove that the class of problems generated by any set of constraints not contained in this restricted set is np complete

constraint satisfaction problems solvable by local consistency methods we prove that constraint satisfaction problems without the ability to count are solvable by the local consistency checking algorithm this settles three equivalent conjectures feder vardi sicomp 98 bulatov lics 04 and larose zadori au 07

a generic arc consistency algorithm and its specializations consistency techniques have been studied extensively in the past as a way of tackling constraint satisfaction problems csp in particular various arc consistency algorithms have been proposed originating from waltz s filtering algorithm and culminating in the optimal algorithm ac 4 of mohr and henderson ac 4 runs in o ed 2 in the worst case where e is the number of arcs or constraints and d is the size of the largest domain being applicable to the whole class of binary csp these algorithms do not take into account the semantics of constraints in this paper we present a new generic arc consistency algorithm ac 5 the algorithm is parameterized on two specified procedures and can be instantiated to reduce to ac 3 and ac 4 more important ac 5 can be instantiated to produce an o ed 2 algorithm for a number of important classes of constraints functional anti functional monotonic and their generalization to functional anti functional and monotonic piecewise constraints we also show that ac 5 has an important application in constraint logic programming over finite domains the kernel of the constraint solver for such a programming language is an arc consistency algorithm for a set of basic constraints we prove that ac 5 in conjuction with node consistency provides a decision procedure for these constraints running in time o ed

tractable constraints on ordered domains abstract finding solutions to a constraint satisfaction problem is known to be an np complete problem in general but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted in this paper we identify a restricted set of contraints which gives rise to a class of tractable problems this class generalizes the notion of a horn formula in propositional logic to larger domain sizes we give a polynomial time algorithm for solving such problems and prove that the class of problems generated by any larger set of constraints is np complete

iterative regularization method in generalized inverse beamforming abstract beamforming based on microphone array is a method to identify sound sources it can visualize the sound field of the source plane and reveal interesting acoustic information generalized inverse beamforming gib is one important branch of beamforming techniques due to its high identification accuracy and computational efficiency however in real testing situation errors caused by measurement noise and configuration problems may seriously reduce the beamforming accuracy as an inverse problem the stability of gib can be improved with regularization methods we proposed a new iterative regularization method for gib by iteratively redefining the form of regularization matrix and calculating the corresponding solution moreover the new method is applied to functional beamforming and double layer antenna beamforming respectively numerical simulations and experiments are implemented the results show that the proposed regularization method leads to more robust beamforming output and higher accuracy in both the two applications

a dichotomy theorem for constraint satisfaction problems on a 3 element set the constraint satisfaction problem csp provides a common framework for many combinatorial problems the general csp is known to be np complete however certain restrictions on a possible form of constraints may affect the complexity and lead to tractable problem classes there is therefore a fundamental research direction aiming to separate those subclasses of the csp that are tractable and those which remain np complete schaefer gave an exhaustive solution of this problem for the csp on a 2 element domain in this article we generalise this result to a classification of the complexity of the csp on a 3 element domain the main result states that every subproblem of the csp is either tractable or np complete and the criterion separating them is that conjectured in bulatov et al 2005 and bulatov and jeavons 2001b we also characterize those subproblems for which standard constraint propagation techniques provide a decision procedure finally we exhibit a polynomial time algorithm which for a given set of allowed constraints outputs if this set gives rise to a tractable problem class to obtain the main result and the algorithm we extensively use the algebraic technique for the csp developed in jeavons 1998b bulatov et al 2005 and bulatov and jeavons 2001b

weak near unanimity functions and digraph homomorphism problems for a fixed digraph h the problem of deciding whether there exists a homomorphism from an input digraph g to h is known as the h colouring problem an algebraic approach to this problem was pioneered by jeavons et al in the context of the more general constraint satisfaction problem results by larose and zadori and by maroti and mckenzie allow one to interpret the algebraic approach in terms of so called weak near unanimity functions wnufs in this paper we focus on weak near unanimity functions and how they apply to the h colouring problem in particular our results range from non existence results of wnufs for certain digraphs h to the existence of wnufs for the well known polynomial cases of the h colouring problem treated by gutjahr woeginger and welzl along the way we develop wnuf analogs of the indicator and sub indicator constructions of hell and nesetril these results provide evidence to the conjecture that weak near unanimity functions are the right measure for the complexity of the h colouring problem

the complexity of quantified constraint satisfaction collapsibility sink algebras and the three element case the constraint satisfaction probem csp is a well acknowledged framework in which many combinatorial search problems can be naturally formulated the csp may be viewed as the problem of deciding the truth of a logical sentence consisting of a conjunction of constraints in front of which all variables are existentially quantified the quantified constraint satisfaction problem qcsp is the generalization of the csp where universal quantification is permitted in addition to existential quantification the general intractability of these problems has motivated research studying the complexity of these problems under a restricted constraint language which is a set of relations that can be used to express constraints this paper introduces collapsibility a technique for deriving positive complexity results on the qcsp in particular this technique allows one to show that for a particular constraint language the qcsp reduces to the csp we show that collapsibility applies to three known tractable cases of the qcsp that were originally studied using disparate proof techniques in different decades quantified 2 sat aspvall plass and tarjan in 1979 quantified horn sat karpinski kleine buning and schmitt in 1987 and quantified affine sat creignou khanna and sudan in 2001 this reconciles and reveals common structure among these cases which are describable by constraint languages over a two element domain in addition to unifying these known tractable cases we study constraint languages over domains of larger size

h coloring dichotomy revisited the h coloring problem can be expressed as a particular case of the constraint satisfaction problem csp whose computational complexity has been intensively studied under various approaches in the last several years we show that the dichotomy theorem proved by hell and neset il on the complexity of h coloring j combin theory ser b 48 1990 92 110 for the complexity of the h coloring problem for undirected graphs can be obtained using general methods for studying csp and that the criterion distinguishing the tractable cases of the h coloring problem agrees with that conjectured in a a bulatov p g jeavons a a krokhin constraint satisfaction problems and finite algebras in proc 27th internat colloq on automata languages and programming icalp 00 lecture notes in computer science vol 1853 springer berlin 2000 pp 272 282 for the complexity of the general csp

support vector machines with constraints for sparsity in the primal parameters this paper introduces a new support vector machine svm formulation to obtain sparse solutions in the primal svm parameters providing a new method for feature selection based on svms this new approach includes additional constraints to the classical ones that drop the weights associated to those features that are likely to be irrelevant a svm formulation has been used where indicates the fraction of features to be considered this paper presents two versions of the proposed sparse classifier a 2 norm svm and a 1 norm svm the latter having a reduced computational burden with respect to the first one additionally an explanation is provided about how the presented approach can be readily extended to multiclass classification or to problems where groups of features rather than isolated features need to be selected the algorithms have been tested in a variety of synthetic and real data sets and they have been compared against other state of the art svm based linear feature selection methods such as 1 norm svm and doubly regularized svm the results show the good feature selection ability of the approaches

full constraint satisfaction problems feder and vardi have conjectured that all constraint satisfaction problems to a fixed structure constraint language are polynomial or np complete this so called dichotomy conjecture remains open although it has been proved in a number of special cases most recently bulatov has verified the conjecture for conservative structures i e structures which contain all possible unary relations we explore three different implications of bulatov s result first the above dichotomy can be extended to so called inclusive structures corresponding to conservative constraint satisfaction problems in which each variable comes with its own domain this has also been independently observed by bulatov we prove a more general version extending the dichotomy to so called three inclusive structures i e structures which contain with any unary relation r all unary relations r for subsets r subseteq r with at most three elements for the constraint satisfaction problems in this generalization we must restrict the instances to so called 1 full structures in which each variable is involved in a unary constraint this leads to our second focus which is on restrictions to more general kinds of full input structures for any set w of positive integers we consider a restriction to w full input structures i e structures in which for each w in w any w variables are involved in a w ary constraint we identify a class of structures the so called w set full structures for which the restriction to w full input structures does not change the complexity of the constraint satisfaction problem and hence the family of these restricted problems also exhibits dichotomy the general family of three inclusive constraint satisfaction problems restricted to w full input structures contains examples which we cannot seem to prove either polynomial or np complete nevertheless we are able to use our result on the dichotomy for three inclusive constraint satisfaction problems to deduce the fact that all three inclusive constraint satisfaction problems restricted to w full input structures are np complete or quasi polynomial of order n o log n our third focus deals with bounding the number of occurrences of a variable which we call the degree we conjecture that the complexity classification of three inclusive constraint satisfaction problems extends to the case where all degrees are bounded by three using previous results we are able to verify this conjecture in a number of special cases conservative inclusive and three inclusive constraint satisfaction problems can be viewed as problems in which each variable is restricted to a list of allowed values this point of view of lists is frequently encountered in the study of graph colorings graph homomorphisms and graph partitions our results presented here in all three areas were strongly motivated by these results on graphs

existentially restricted quantified constraint satisfaction the quantified constraint satisfaction problem qcsp is a framework for modelling pspace computational problems the general intractability of the qcsp has motivated the pursuit of restricted cases that avoid its maximal complexity in this paper we introduce and study a new model for investigating qcsp complexity in which the types of constraints given by the existentially quantified variables is restricted our primary technical contribution is the development and application of a general technology for proving positive results on parameterizations of the model of inclusion in the complexity class conp

the power of linear programming for general valued csps let d called the domain be a fixed finite set and let gamma called the valued constraint language be a fixed set of functions of the form f d m to mathbb q cup infty where different functions might have different arity m we study the valued constraint satisfaction problem parametrized by gamma denoted by vcsp gamma these are minimization problems given by n variables and the objective function given by a sum of functions from gamma each depending on a subset of the n variables for example if d 0 1 and gamma contains all ternary 0 infty valued functions vcsp gamma corresponds to 3 sat more generally if gamma contains only 0 infty valued functions vcsp gamma corresponds to csp gamma if d 0 1 and gamma contains all ternary 0 1 valued functions vcsp gamma corresponds to min 3 sat in which the goal is to minimize the number of unsatisfied clauses in a 3 cnf instance finite valued constraint languages contain functions that take on only rational values and not infinite values our main result is a precise algebraic characterization of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation blp for a valued constraint language gamma blp is a decision procedure for gamma if and only if gamma admits a symmetric fractional polymorphism of every arity for a finite valued constraint language gamma blp is a decision procedure if and only if gamma admits a symmetric fractional polymorphism of some arity or equivalently if gamma admits a symmetric fractional polymorphism of arity 2 using these results we obtain tractability of several novel classes of problems including problems over valued constraint languages that are 1 submodular on arbitrary lattices 2 k submodular on arbitrary finite domains 3 weakly and hence strongly tree submodular on arbitrary trees

a sufficient condition for backtrack bounded search backtrack search is often used to solve constraint satisfaction problems a relationship involving the structure of the constraints is described that provides a bound on the backtracking required to advance deeper into the backtrack tree this analysis leads to upper bounds on the effort required for solution of a class of constraint satisfaction problems the solutions involve a combination of relaxation preprocessing and backtrack search the bounds are expressed in terms of the structure of the constraint connections specifically the effort is shown to have a bound exponential in the size of the largest biconnected component of the constraint graph as opposed to the size of the graph as a whole

gap theorems for robust satisfiability boolean csps and beyond abstract a computational problem exhibits a gap property when there is no tractable boundary between two disjoint sets of instances we establish a gap trichotomy theorem for a family of constraint problem variants completely classifying the complexity of possible np hard gaps in the case of boolean domains as a consequence we obtain a number of dichotomies for the complexity of specific variants of the constraint satisfaction problem all are either polynomial time tractable or np complete schaefer s original dichotomy for sat variants is a notable particular case universal algebraic methods have been central to recent efforts in classifying the complexity of constraint satisfaction problems a second contribution of the article is to develop aspects of the algebraic approach in the context of a number of variants of the constraint satisfaction problem in particular this allows us to lift our results on boolean domains to many templates on non boolean domains

addendum regularization and variable selection via the elastic net we missed an important reference in section 3 4 in page 309 we stated that which is based on the recently proposed algorithm lars of efron et al 2004 they proved that starting from zero the lasso solution paths grow piecewise linearly in a predictable way they proposed a new algorithm called lars to solve the entire lasso solution path efficiently by using the same order of computations as a single ols fit the following sentence should have been included the piecewise linearity of the lasso solution path was first proved by osborne et al 2000 who also described an efficient algorithm for calculating the complete lasso solution path reference osborne m r presnell b and turlach b a 2000 a new approach to variable selection in least squares problems ima j numer anal 20 389 403

decomposing constraint satisfaction problems using database techniques abstract there is a very close relationship between constraint satisfaction problems and the satisfaction of join dependencies in a relational database which is due to a common underlying structure namely a hypergraph by making that relationship explicit we are able to adapt techniques previously developed for the study of relational databases to obtain new results for constraint satisfaction problems in particular we prove that a constraint satisfaction problem may be decomposed into a number of subproblems precisely when the corresponding hypergraph satisfies a simple condition we show that combining this decomposition approach with existing algorithms can lead to a significant improvement in efficiency

the complexity of approximating bounded degree boolean csp the degree of a csp instance is the maximum number of times that any variable appears in the scopes of constraints we consider the approximate counting problem for boolean csp with bounded degree instances for constraint languages containing the two unary constant relations 0 and 1 when the maximum allowed degree is large enough at least 6 we obtain a complete classification of the complexity of this problem it is exactly solvable in polynomial time if every relation in the constraint language is affine it is equivalent to the problem of approximately counting independent sets in bipartite graphs if every relation can be expressed as conjunctions of 0 1 and binary implication otherwise there is no fpras unless np rp for lower degree bounds additional cases arise where the complexity is related to the complexity of approximately counting independent sets in hypergraphs

some error estimates for the numerical approximation of surface integrals recently the first author introduced a new approach to the numeri cal quadrature of surface integrals in the context of boundary element methods it is assumed that a global parametrization m of the surface is only indirectly given e g via an iterative method and that m is not accessible analytically of particular interest are parametrizations which are based on automatic tri angulations of surfaces in order to avoid an explicit reference to the partial derivatives of m modified trapezoidal and midpoint rules were introduced the present paper discusses some error estimates for these methods the esti mates are surprisingly difficult since cf i3 terms have to be shown to cancel this does not occur in the expansion of the standard rules

a new proof of the euler maclaurin expansion for quadrature over implcitly defined curves in this paper we describe and justify a method for integrating over implicitly defined curves this method does not require that the jacobian be known explicitly we give a proof of an asymptotic error expansion for this method which is a modification of that of lyness 4

recognizing frozen variables in constraint satisfaction problems in constraint satisfaction problems over finite domains some variables can be frozen that is they take the same value in all possible solutions we study the complexity of the problem of recognizing frozen variables with restricted sets of constraint relations allowed in the instances we show that the complexity of such problems is determined by certain algebraic properties of these relations under the assumption that np conp and consequently ptime np we characterize all tractable problems and describe large classes of np complete conp complete and dp complete problems as an application of these results we completely classify the complexity of the problem in two cases 1 with domain size 2 and 2 when all unary relations are present we also give a rough classification for domain size 3

maximal infinite valued constraint languages we systematically investigate the computational complexity of constraint satisfaction problems for constraint languages over an infinite domain in particular we study a generalization of the well established notion of maximal constraint languages from finite to infinite domains if the constraint language can be defined with an w categorical structure then maximal constraint languages are in one to one correspondence to minimal oligomorphic clones based on this correspondence we derive general tractability and hardness criteria for the corresponding constraint satisfaction problems

the complexity of soft constraint satisfaction over the past few years there has been considerable progress in methods to systematically analyse the complexity of constraint satisfaction problems with specified constraint types one very powerful theoretical development in this area links the complexity of a set of constraints to a corresponding set of algebraic operations known as polymorphisms in this paper we extend the analysis of complexity to the more general framework of combinatorial optimisation problems expressed using various forms of soft constraints we launch a systematic investigation of the complexity of these problems by extending the notion of a polymorphism to a more general algebraic operation which we call a multimorphism we show that many tractable sets of soft constraints both established and novel can be characterised by the presence of particular multimorphisms we also show that a simple set of np hard constraints has very restricted multimorphisms finally we use the notion of multimorphism to give a complete classification of complexity for the boolean case which extends several earlier classification results for particular special cases

the complexity of conservative valued csps we study the complexity of valued constraint satisfaction problems vcsps parametrized by a constraint language a fixed set of cost functions over a finite domain an instance of the problem is specified by a sum of cost functions from the language and the goal is to minimize the sum under the unique games conjecture the approximability of finite valued vcsps is well understood see raghavendra 2008 however there is no characterization of finite valued vcsps let alone general valued vcsps that can be solved exactly in polynomial time thus giving insights from a combinatorial optimization perspective we consider the case of languages containing all possible unary cost functions in the case of languages consisting of only 0 valued cost functions i e relations such languages have been called conservative and studied by bulatov 2003 2011 and recently by barto 2011 since we study valued languages we call a language conservative if it contains all finite valued unary cost functions the computational complexity of conservative valued languages has been studied by cohen et al 2006 for languages over boolean domains by deineko et al 2008 for 0 1 valued languages a k a max csp and by takhanov 2010a for 0 valued languages containing all finite valued unary cost functions a k a min cost hom we prove a schaefer like dichotomy theorem for conservative valued languages if all cost functions in the language satisfy a certain condition specified by a complementary combination of stp and mjn multimorphisms then any instance can be solved in polynomial time via a new algorithm developed in this article otherwise the language is np hard this is the first complete complexity classification of general valued constraint languages over non boolean domains it is a common phenomenon that complexity classifications of problems over non boolean domains are significantly harder than the boolean cases the polynomial time algorithm we present for the tractable cases is a generalization of the submodular minimization problem and a result of cohen et al 2008 our results generalize previous results by takhanov 2010a and a subset of results by cohen et al 2006 and deineko et al 2008 moreover our results do not rely on any computer assisted search as in deineko et al 2008 and provide a powerful tool for proving hardness of finite valued and general valued languages

numerical integration with taylor truncations for the quadrilateral and hexahedral finite elements for general quadrilateral or hexahedral meshes the finite element methods require evaluation of integrals of rational functions instead of traditional polynomials it remains as a challenge in mathematics to show the traditional gauss quadratures would ensure the correct order of approximation for the numerical integration in general however in the case of nested refinement the refined quadrilaterals and hexahedra converge to parallelograms and parallelepipeds respectively based on this observation the rational functions of inverse jacobians can be approximated by the taylor expansion with truncation then the gauss quadrature of exact order can be adopted for the resulting integrals of polynomials retaining the optimal order approximation of the finite element methods a theoretic justification and some numerical verification are provided in the paper

quadrature methods for 2d and 3d problems in this paper we give an overview on well known stability and convergence results for simple quadrature methods based on low order composite quadrature rules and applied to the numerical solution of integral equations over smooth manifolds first we explain the methods for the case of second kind equations then we discuss what is known for the analysis of pseudodifferential equations we explain why these simple methods are not recommended for integral equations over domains with dimension higher than one finally for the solution of a two dimensional singular integral equation we prove a new result on a quadrature method based on product rules

forecasting economic time series using targeted predictors abstract this paper studies two refinements to the method of factor forecasting first we consider the method of quadratic principal components that allows the link function between the predictors and the factors to be non linear second the factors used in the forecasting equation are estimated in a way to take into account that the goal is to forecast a specific series this is accomplished by applying the method of principal components to targeted predictors selected using hard and soft thresholding rules our three main findings can be summarized as follows first we find improvements at all forecast horizons over the current diffusion index forecasts by estimating the factors using fewer but informative predictors allowing for non linearity often leads to additional gains second forecasting the volatile one month ahead inflation warrants a high degree of targeting to screen out the noisy predictors a handful of variables notably relating to housing starts and interest rates are found to have systematic predictive power for inflation at all horizons third the targeted predictors selected by both soft and hard thresholding changes with the forecast horizon and the sample period holding the set of predictors fixed as is the current practice of factor forecasting is unnecessarily restrictive

properties of tree convex constraints it is known that a tree convex network is globally consistent if it is path consistent however if a tree convex network is not path consistent enforcing path consistency on it may not make it globally consistent in this paper we investigate the properties of some tree convex constraints under intersection and composition as a result we identify a sub class of tree convex networks that are locally chain convex and strictly union closed this class of problems can be made globally consistent by arc and path consistency and thus is tractable interestingly we also find that some scene labeling problems can be modeled by tree convex constraints in a natural and meaningful way

constraint satisfaction logic and forbidden patterns in the 1990s feder and vardi attempted to find a large subclass of np which exhibits a dichotomy that is where every problem in the subclass is either solvable in polynomial time or np complete their studies resulted in a candidate class of problems namely those definable in the logic mmsnp while it remains open as to whether mmsnp exhibits a dichotomy for various reasons it remains a strong candidate feder and vardi added to the significance of mmsnp by proving that although mmsnp strictly contains csp the class of constraint satisfaction problems mmsnp and csp are computationally equivalent we introduce here a new class of combinatorial problems the class of forbidden patterns problems fpp and characterize mmsnp as the finite unions of problems from fpp we use our characterization to detail exactly those problems that are in mmsnp but not in csp furthermore given a problem in mmsnp we are able to decide whether the problem is in csp or not this whole process is effective if the problem is in csp then we can construct a template for this problem otherwise for any given candidate for the role of template we can build a counterexample again this process is effective

binary constraint satisfaction problems defined by excluded topological minors abstract the binary constraint satisfaction problem csp is to decide whether there exists an assignment to a set of variables which satisfies specified constraints between pairs of variables a binary csp instance can be presented as a labelled graph encoding both the forms of the constraints and where they are imposed we consider subproblems defined by restricting the allowed form of this graph one type of restriction is to forbid certain specified substructures patterns this captures some tractable classes of the csp but does not capture classes defined by language restrictions or the well known structural property of acyclicity we extend the notion of pattern and introduce the notion of a topological minor of a binary csp instance by forbidding a finite set of patterns from occurring as topological minors we obtain a compact mechanism for expressing novel tractable subproblems of the csp including new generalisations of the class of acyclic instances

closure properties of constraints many combinatorial search problems can be expressed as constraint satisfaction problems and this class of problems is known to be np complete in general in this paper we investigate the subclasses that arise from restricting the possible constraint types we first show that any set of constraints that does not give rise to an np complete class of problems must satisfy a certain type of algebraic closure condition we then investigate all the different possible forms of this algebraic closure property and establish which of these are sufficient to ensure tractability as examples we show that all known classes of tractable constraints over finite domains can be characterized by such an algebraic closure property finally we describe a simple computational procedure that can be used to determine the closure properties of a given set of constraints this procedure involves solving a particular constraint satisfaction problem which we call an indicator problem

the complexity of homomorphism and constraint satisfaction problems seen from the other side we give a complexity theoretic classification of homomorphism problems for graphs and more generally relational structures obtained by restricting the left hand side structure in a homomorphism for every class c of structures let hom c be the problem of deciding whether a given structure a c has a homomorphism to a given arbitrary structure s we prove that under some complexity theoretic assumption from parameterized complexity theory hom c is in polynomial time if and only if c has bounded tree width modulo homomorphic equivalence translated into the language of constraint satisfaction problems our result yields a characterization of the tractable structural restrictions of constraint satisfaction problems translated into the language of database theory it implies a characterization of the tractable instances of the evaluation problem for conjunctive queries over relational databases

building tractable disjunctive constraints many combinatorial search problems can be expressed as constraint satisfaction problems this class of problems is known to be np hard in general but a number of restricted constraint classes have been identified which ensure tractability this paper presents the first general results on combining tractable constraint classes to obtain larger more general tractable classes we give examples to show that many known examples of tractable constraint classes from a wide variety of different contexts can be constructed from simpler tractable classes using a general method we also construct several new tractable classes that have not previously been identified

a simple algorithm for mal tsev constraints a mal tsev operation is a ternary operation varphi that satisfies the identities varphi x y y varphi y y x x constraint satisfaction problems involving constraints invariant under a mal tsev operation constitute an important class of constraint satisfaction problems which includes the affine satisfiability problem subgroup and near subgroup constraints and many others it is also known that any tractable case of the counting constraint satisfaction problem involves only mal tsev constraints the first algorithm solving the arbitrary constraint satisfaction problem with mal tsev constraints has been given by bulatov however this algorithm is very sophisticated and relies heavily on advanced algebraic machinery in this paper we give a different and much simpler algorithm for this type of constraint

affine systems of equations and counting infinitary logic we study the definability of constraint satisfaction problems csps in various fixed point and infinitary logics we show that testing the solvability of systems of equations over a finite abelian group a tractable csp that was previously known not to be definable in datalog is not definable in the infinitary logic with finitely many variables and counting this implies that it is not definable in least fixed point logic or its extension with counting we relate definability of csps to their classification obtained from tame congruence theory of the varieties generated by the algebra of polymorphisms of the template structure in particular we show that if this variety admits either the unary or affine type the corresponding csp is not definable in the infinitary logic with counting

on binary constraint problems the concepts of binary constraint satisfaction problems can be naturally generalized to the relation algebras of tarski the concept of path consistency plays a central role algorithms for path consistency can be implemented on matrices of relations and on matrices of elements from a relation algebra we give an example of a 4 by 4 matrix of infinite relations on which on iterative local path consistency algorithm terminates we give a class of examples over a fixed finite algebra on which all iterative local algorithms whether parallel or sequential must take quadratic time specific relation algebras arising from interval constraint problems are also studied the interval algebra the point algebra and the containment algebra

the complexity of temporal constraint satisfaction problems a temporal constraint language is a set of relations that has a first order definition in q an extended abstract of this article appeared in the proceedings of stoc 08

high order numerical integration over discrete surfaces we consider the problem of numerical integration of a function over a discrete surface to high order accuracy surface integration is a common operation in numerical computations for scientific and engineering problems integration over discrete surfaces such as a surface triangulation is typically limited to first or second order accuracy due to the piecewise linear approximations of the surface and the function we present a novel method that can achieve third and higher order accuracy for integration over discrete surfaces our method combines a stabilized least squares approximation a blending procedure based on linear shape functions and high degree quadrature rules we present theoretical analysis of the accuracy of our method as well as experimental results of up to sixth order accuracy with our method

a dichotomy theorem for the approximate counting of complex weighted bounded degree boolean csps we determine the computational complexity of approximately counting the total weight of variable assignments for every complex weighted boolean constraint satisfaction problem or csp with any number of additional unary i e arity 1 constraints particularly when degrees of input instances are bounded from above by a fixed constant all degree 1 counting csps are obviously solvable in polynomial time when the instance s degree is more than two we present a dichotomy theorem that classifies all counting csps admitting free unary constraints into exactly two categories this classification theorem extends to complex weighted problems an earlier result on the approximation complexity of unweighted counting boolean csps of bounded degree the framework of the proof of our theorem is based on a theory of signature developed from valiant s holographic algorithms that can efficiently solve seemingly intractable counting csps despite the use of arbitrary complex weight our proof of the classification theorem is rather elementary and intuitive due to an extensive use of a novel notion of limited t constructibility for the remaining degree 2 problems in contrast they are as hard to approximate as holant problems which are a generalization of counting csps

quadrature over curved surfaces by extrapolation in this paper the authors describe and justify a method for integrating over curved surfaces this method does not require that the jacobian be known explicitly this is a natural extension of extrapolation or romberg integration for planar squares or triangles 9 refs

schaefer s theorem for graphs schaefer s theorem is a complexity classification result for so called boolean constraint satisfaction problems it states that every boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in polynomial time or is np complete we present an analog of this dichotomy result for the propositional logic of graphs instead of boolean logic in this generalization of schaefer s result the input consists of a set w of variables and a conjunction of statements constraints about these variables in the language of graphs where each statement is taken from a fixed finite set of allowed quantifier free first order formulas the question is whether is satisfiable in a graph we prove that either is contained in one out of 17 classes of graph formulas and the corresponding problem can be solved in polynomial time or the problem is np complete this is achieved by a universal algebraic approach which in turn allows us to use structural ramsey theory to apply the universal algebraic approach we formulate the computational problems under consideration as constraint satisfaction problems csps whose templates are first order definable in the countably infinite random graph our method for classifying the computational complexity of those csps is based on a ramsey theoretic analysis of functions acting on the random graph and we develop general tools suitable for such an analysis which are of independent mathematical interest

the complexity of acyclic conjunctive queries this paper deals with the evaluation of acyclic booleanconjunctive queries in relational databases by well known resultsof yannakakis 1981 this problem is solvable in polynomial time its precise complexity however has not been pinpointed so far weshow that the problem of evaluating acyclic boolean conjunctivequeries is complete for logcfl the class of decision problems thatare logspace reducible to a context free language since logcfl iscontained in ac1 and nc2 the evaluation problem of acyclic booleanconjunctive queries is highly parallelizable we present a paralleldatabase algorithm solving this problem with alogarithmic number ofparallel join operations the algorithm is generalized to computingthe output of relevant classes of non boolean queries we also showthat the acyclic versions of the following well known database andai problems are all logcfl complete the query output tuple problemfor conjunctive queries conjunctive query containment clausesubsumption and constraint satisfaction the logcfl completenessresult is extended to the class of queries of bounded tree widthand to other relevant query classes which are more general than theacyclic queries

fast parallel constraint satisfaction a constraint satisfaction problem csp involves searching for an assignment of values to a given set of variables so that the values assigned satisfy a given set of constraints the general csp is np complete to confront the intractability of the general csp relaxation procedures have been devised instead of searching for a globally consistent assignment of values to the variables try to restrict the domain of values of each variable in a way that ensures local consistency only the relaxation procedures are efficient but have been proved to be inherently sequential in this paper we define a class of csps for which a global solution can be found by a fast parallel algorithm no relaxation preprocessing is needed for the parallel algorithm to work the result is motivated from the problem of labelling a 2 d line drawing of a 3 d object by the clowes huffman malik labelling scheme an important application of csp in computer vision for such a labelling csp the constraint graph can be general but the constraint relations are usually of the type we call implicational it is shown here that a csp with this type of constraint relations and no restrictions on its graph can be solved by an efficient i e with polynomial time complexity sequential algorithm also it is shown that it can be solved by a fast parallel algorithm that executes in time o log3n with o m n3 log n processors on a exlusive read exclusive write parallel random access machine n is the number of variables and m is the number of constrain relations the constraint relations may have arity more than two

the computational structure of monotone monadic snp and constraint satisfaction a study through datalog and group theory this paper starts with the project of finding a large subclass of np which exhibits a dichotomy the approach is to find this subclass via syntactic prescriptions while the paper does not achieve this goal it does isolate a class of problems specified by monotone monadic snp without inequality which may exhibit this dichotomy we justify the placing of all these restrictions by showing essentially using ladner s theorem that classes obtained by using only two of the above three restrictions do not show this dichotomy we then explore the structure of this class we show that all problems in this class reduce to the seemingly simpler class csp we divide csp into subclasses and try to unify the collection of all known polytime algorithms for csp problems and extract properties that make csp problems np hard this is where the second part of the title a study through datalog and group theory comes in we present conjectures about this class which would end in showing the dichotomy

implicit methods of solution to integral formulations in boundary element method based nearfield acoustic holography two integral equation methods are considered which can be inverted to provide the surface velocity and or pressure given a measurement of the pressure on an imaginary surface in the nearfield of a vibrating or scattering body this problem is central to nearfield acoustical holography nah the integral equations are discretized using boundary element methods bems the integral equation methods considered are 1 an indirect formulation method based on the single layer integral equation and 2 a direct formulation method based on a system of equations derived from the helmholtz kirchhoff integral equation the formation of integral equations from the mentioned methods will not involve the explicit inversion of matrices but instead will require this inversion to be done implicitly since these methods back track the sound field from the measurement surface to the surface of the source vibrator they are ill posed in nature and tikhonov regularization are used to stabilize the reconstruction problems a

structure identification in relational data this paper presents several investigations into the prospects for identifying meaningful structures in empirical data namely structures permitting effective organization of the data to meet requirements of future queries we propose a general framework whereby the notion of identifiability is given a precise formal definition similar to that of learnability using this framework we then explore if a tractable procedure exists for deciding whether a given relation is decomposable into a constraint network or a cnf theory with desirable topology and if the answer is positive identifying the desired decomposition finally we address the problem of expressing a given relation as a horn theory and if this is impossible finding the best k horn approximation to the given relation we show that both problems can be solved in time polynomial in the length of the data

constructing np intermediate problems by blowing holes with parameters of various properties the search for natural np intermediate problems is one of the holy grails within computational complexity ladner s original diagonalization technique for generating np intermediate problems blowing holes has a serious shortcoming it creates problems with a highly artificial structure by arbitrarily removing certain problem instances in this article we limit this problem by generalizing ladner s method to use parameters with various characteristics this allows one to define more fine grained parameters resulting in np intermediate problems where we only blow holes in a controlled subset of the problem we begin by fully characterizing the problems that admit np intermediate subproblems for a broad and natural class of parameterizations and extend the result further such that structural csp restrictions based on parameters that are hard to compute such as tree width are covered thereby generalizing a result by grohe for studying certain classes of problems including csps parameterized by constraint languages we consider more powerful parameterizations first we identify a new method for obtaining constraint languages such that csp are np intermediate the sets can have very different properties compared to previous constructions by for instance bodirsky grohe and provides insights into the algebraic approach for studying the complexity of infinite domain csps second we prove that the propositional abduction problem parameterized by constraint languages admits np intermediate problems this settles an open question posed by nordh zanuttini we provide a framework to obtain np intermediate problems based on diagonalization we categorize different types of parameters that are usable in our framework we construct np intermediate constraint satisfaction problems we resolve the open question whether boolean abduction admits intermediate problems

tractable hypergraph properties for constraint satisfaction and conjunctive queries 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 that is 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 grohe 2007 marx 2010b 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 evaluation problems in database theory formally if h is a class of hypergraphs then let csp h be csp restricted to instances whose hypergraph is in h our goal is to characterize those classes of hypergraphs for which csp h is polynomial time solvable or fixed parameter tractable parameterized by the number of variables note that in the applications related to database query evaluation we usually assume that the number of variables is much smaller than the size of the instance thus parameterization by the number of variables is a meaningful question the most general known property of h that makes csp h polynomial time solvable is bounded fractional hypertree width here we introduce a new hypergraph measure called submodular width and show that bounded submodular width of h which is a strictly more general property than bounded fractional hypertree width implies that csp h is fixed parameter tractable in a matching hardness result we show that if h has unbounded submodular width then csp h is not fixed parameter tractable and hence not polynomial time solvable unless the exponential time hypothesis eth fails the algorithmic result uses tree decompositions in a novel way instead of using a single decomposition depending on the hypergraph the instance is split into a set of instances all on the same set of variables as the original instance and then the new instances are solved by choosing a different tree decomposition for each of them the reason why this strategy works is that the splitting can be done in such a way that the new instances are uniform with respect to the number extensions of partial solutions and therefore the number of partial solutions can be described by a submodular function for the hardness result we prove via a series of combinatorial results that if a hypergraph h has large submodular width then a 3sat instance can be efficiently simulated by a csp instance whose hypergraph is h to prove these combinatorial results we need to develop a theory of multicommodity flows on hypergraphs and vertex separators in the case when the function b s defining the cost of separator s is submodular which can be of independent interest

qualitative constraint satisfaction problems an extended framework with landmarks dealing with spatial and temporal knowledge is an indispensable part of almost all aspects of human activity the qualitative approach to spatial and temporal reasoning known as qualitative spatial and temporal reasoning qstr typically represents spatial temporal knowledge in terms of qualitative relations e g to the east of after and reasons with spatial temporal knowledge by solving qualitative constraints when formulating qualitative constraint satisfaction problems csps it is usually assumed that each variable could be here there and everywhere practical applications such as urban planning however often require a variable to take its value from a certain finite domain i e it is required to be here or there but not everywhere entities in such a finite domain often act as reference objects and are called landmarks in this paper the paper extends the classical framework of qualitative csps by allowing variables to take values from finite domains the computational complexity of the consistency problem in this extended framework is examined for the five most important qualitative calculi viz point algebra interval algebra cardinal relation algebra rcc5 and rcc8 we show that all these consistency problems remain in np and provide under practical assumptions efficient algorithms for solving basic constraints involving landmarks for all these calculi

from local to global consistency abstract in reasoning tasks involving the maintenance of consistent databases so called qqconstraint networks q q it is customary to enforce local consistency conditions in order to simplify the subsequent construction of a globally coherent model of the data in this paper we present a relationship between the sizes of the variables domains the constraints arity and the level of local consistency sufficient to ensure global consistency based on these parameters a new tractability classification of constraint networks is presented we also show based on this relationship that any relation on bi valued variables which is not representable by a network of binary constraints cannot be represented by networks with any number of hidden variables

fanout limitations on constraint systems we examine several families of constraint systems constraint satisfaction and network stability are well understood network stability was introduced in an attempt to understand the role of fanout we introduce two new families of constraint systems in a new attempt to limit fanout these two families are graph constraint satisfaction and bipartite constraint satisfaction we obtain the following results 1 an extension of schaefer s classification argument for boolean satisfiability to boolean graph constraint satisfaction and bipartite constraint satisfaction 2 a characterization of the graph constraint satisfaction problems that lack fanout in terms of a new problem the generalized matroid parity problem which gives rise to many new problems whose complexity is yet to be determined in particular the coindependent set problem is shown to be polynomial and 3 generalized matroid intersection characterizes the lack of fanout in the bipartite case with a family of matroid intersection problems as a special polynomially solvable subcase

efficient algorithms for description problems over finite totally ordered domains given a finite set of vectors over a finite totally ordered domain we study the problem of computing a constraint in conjunctive normal form such that the set of solutions for the produced constraint is identical to the original set we develop an efficient polynomial time algorithm for the general case followed by specific polynomial time algorithms producing horn dual horn and bijunctive formulas for sets of vectors closed under the operations of conjunction disjunction and median respectively our results generalize the work of dechter and pearl on relational data as well as the papers by hebrard and zanuttini they complement the results of hahnle et al on multivalued logics and jeavons et al on the algebraic approach to constraints

numerical quadrature over smooth closed surfaces the numerical approximation of definite integrals or quadrature often involves the construction of an interpolant of the integrand and its subsequent integration in the case of one dimension it is natural to rely on polynomial interpolants however their extension to two or more dimensions can be costly and unstable an efficient method for computing surface integrals on the sphere is detailed in the literature reeger fornberg 2016 stud appl math 137 174 188 doi 10 1111 sapm 12106 the method uses local radial basis function interpolation to reduce computational complexity when generating quadrature weights for any given node set this article generalizes this method to arbitrary smooth closed surfaces