the complexity of constraint satisfaction revisited abstract this paper is a retrospective account of some of the developments leading up to and ensuing from the analysis of the complexity of some polynomial network consistency algorithms for constraint satisfaction problems

on error estimates of the penalty method for unsteady navier stokes equations the penalty method has been widely used for numerical computations of the unsteady navier stokes equations however the best error estimates available to the author s knowledge were not optimal an

a modified weak galerkin finite element method for a class of parabolic problems in this paper we consider the solution of parabolic equation using the modified weak galerkin finite element procedure which is named as mwg fem based on the conception of the modified weak derivative over discontinuous functions with heterogeneous properties in which the classical gradient operator is replaced by a modified weak gradient operator optimal order error estimates in a discrete l2 norm and h1 norm are established for the corresponding modified weak galerkin finite element solutions finally we numerically verify the convergence theory for the mwg fem through some examples

local consistency in parallel constraint satisfaction networks abstract in this paper we present several basic techniques for achieving parallel execution of constraint networks the major result supported by our investigations is that the parallel complexity of constraint networks is critically dependent on subtle properties of the network that do not influence its sequential complexity

compaction retraction and constraint satisfaction in this paper we show a very close relationship among the compaction retraction and constraint satisfaction problems in the context of reflexive and bipartite graphs the compaction and retraction problems are special graph coloring problems and the constraint satisfaction problem is well known to have an important role in artificial intelligence the relationships we present provide evidence that similar to as for the retraction problem it is likely to be difficult to determine whether for every fixed reflexive or bipartite graph the compaction problem is polynomial time solvable or np complete in particular the relationships that we present relate to a long standing open problem concerning the equivalence of the compaction and retraction problems

uncovering trees in constraint networks abstract this paper examines the possibility of removing redundant information from a given knowledge base and restructuring it in the form of a tree to enable efficient problem solving routines we offer a novel approach that guarantees removal of all redandancies that hide a tree structure we develop a polynomial time algorithm that given an arbitrary binary constraint network either extracts by edge removal a precise tree representation from the path consistent version of the network or acknowledges that no such tree can be extracted in the latter case a tree is generated that may serve as an approximation to the original network

temporal constraint networks abstract this paper extends network based methods of constraint satisfaction to include continuous variables thus providing a framework for processing temporal constraints in this framework called temporal constraint satisfaction problem tcsp variables represent time points and temporal information is represented by a set of unary and binary constraints each specifying a set of permitted intervals the unique feature of this framework lies in permitting the processing of metric information namely assessments of time differences between events we present algorithms for performing the following reasoning tasks finding all feasible times that a given event can occur finding all possible relationships between two given events and generating one or more scenarios consistent with the information provided we distinguish between simple temporal problems stps and general temporal problems the former admitting at most one interval constraint on any pair of time points we show that the stp which subsumes the major part of vilain and kautz s point algebra can be solved in polynomial time for general tcsps we present a decomposition scheme that performs the three reasoning tasks considered and introduce a variety of techniques for improving its efficiency we also study the applicability of path consistency algorithms as preprocessing of temporal problems demonstrate their termination and bound their complexities

integer programs for logic constraint satisfaction abstract logic constraint satisfaction problems are in general np hard and a general deterministic polynomial time algorithm is not known since several logic constraint problems can be reduced in polynomial time to the satisfaction of a conjunctive normal form cnf sat this case is very important we present here a technique to transform a cnf sat problem in an integer optimization problem that can be solved by linear programming the size of the obtained integer program has a polynomial growth in comparison with the original problem size

a modified weak galerkin finite element method in this paper we introduce a new discrete weak gradient operator and a new weak galerkin wg finite element method for second order poisson equations based on this new operator this newly defined discrete weak gradient operator allows us to use a single stabilizer which is similar to the one used in the discontinuous galerkin dg methods without having to worry about choosing a sufficiently large parameter in addition we will establish the optimal convergence rates and validate the results with numerical examples

constraint satisfaction problem with bilevel constraint application to interpretation of over segmented images abstract in classical finite domain constraint satisfaction problems the assumption made is that only one value is associated with only one variable for example in pattern recognition one variable is associated with only one segmented region however in practice regions are often oversegmented which results in failure of any one to one mapping this paper proposes a definition of finite domain constraint satisfaction problems with bilevel constraints in order to take into account a many to one relation between the values and the variables the additional level of constraint concerns the data assigned to the same complex variable then we give a definition of the arc consistency problem for bilevel constraint satisfaction checking a new algorithm for arc consistency to deal with these problems is presented as well this extension of the arc consistency algorithm retains its good properties and has a time complexity in o en 3 d 2 in the worst case this algorithm was tested on medical images these tests demonstrate its reliability in correctly identifying the segmented regions even when the image is over segmented

the complexity of some polynomial network consistency algorithms for constraint satisfaction problems abstract constraint satisfaction problems play a central role in artificial intelligence a class of network consistency algorithms for eliminating local inconsistencies in such problems has previously been described we analyze the time complexity of several node arc and path consistency algorithms and prove that arc consistency is achievable in time linear in the number of binary constraints the waltz filtering algorithm is a special case of the arc consistency algorithm in the edge labelling computational vision application the constraint graph is planar and so the time complexity is linear in the number of variables

incremental qualitative temporal reasoning algorithms for the point algebra and the ord horn class in many applications of temporal reasoning we are interested in processing temporal information incrementally in particular given a set of temporal constraints a temporal csp and a new constraint we want to maintain certain properties of the extended temporal csp e g a solution rather than recomputing them from scratch the point algebra pa and the interval algebra ia are two well known frameworks for qualitative temporal reasoning the reasoning algorithms for pa and the tractable fragments of ia such as nebel and burckert s maximal tractable class of relations ord horn have originally been designed for static reasoning in this paper we study the incremental version of the fundamental reasoning problems in the context of these tractable classes we propose a collection of new polynomial algorithms that can amortize their complexity when processing a sequence of input constraints to incrementally decide satisfiability to maintain a solution or to update the minimal representation of the csp our incremental algorithms improve the total time complexity of using existing static techniques by a factor of o n or o n2 where n is the number of the variables involved by the temporal csp an experimental analysis focused on constraints over pa confirms the computational advantage of our incremental approach

arc consistency for factorable relations abstract an optimal arc consistency algorithm ac 4 was given by mohr and henderson 8 ac 4 has cost o ed 2 and cost nd 2 for scene labelling although their algorithm is indeed optimal under certain conditions a constraint satisfaction problem can be transformed into a less complex problem in this paper we present conditions and mechanisms for such representational transformations and show how to factor relations into more manageable components we describe how factorization can reduce ac 4 s cost to o ed and apply this result to rete match further with our factorization the cost of scene labelling is reduced to o nd

on the asymptotic complexity of matrix multiplication the main results of this paper have the following flavor given one algorithm for multiplying matrices there exists another better algorithm a consequence of these results is that omega the exponent for matrix multiplication is a limit point that is it cannot be realized by any single algorithm we also use these results to construct a new algorithm which shows that omega 2 495548

constraint reasoning based on interval arithmetic the tolerance propagation approach abstract interval constraint satisfaction interval labeling systems have traditionally been based on local waltz filtering techniques that cannot in general determine global solutions in contrast this paper documents a related technique tolerance propagation tp that generalizes the idea of numerical exact value propagation into interval propagation in tp consistency techniques based on the topology of the constraint net can be combined with techniques of interval arithmetic in a new fruitful way in particular by tp it is possible to determine global solutions for interval constraint satisfaction problems with arbitrary accuracy and without losing all attractions of simple local computations

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

network based heuristics for constraint satisfaction problems abstract many ai tasks can be formulated as constraint satisfaction problems csp i e the assignment of values to variables subject to a set of constraints while some csps are hard those that are easy can often be mapped into sparse networks of constraints which in the extreme case are trees this paper identifies classes of problems that lend themselves to easy solutions and develops algorithms that solve these problems optimally the paper then presents a method of generating heuristic advice to guide the order of value assignments based on both the sparseness found in the constraint network and the simplicity of tree structured csps the advice is generated by simplifying the pending subproblems into trees counting the number of consistent solutions in each simplified subproblem and comparing these counts to decide among the choices pending in the original problem

constraint satisfaction neural networks for image segmentation abstract constraint satisfaction neural networks csnns are proposed for image recognition which is the process to identify objects of interest in an image the image recognition problem is formulated as a constraint satisfaction problem csp the regions resulting from a signal based image segmentation algorithm can be considered as objects and their entities as labels in the csp the proposed neural network is multi layered and the function of each layer is to identify one physical entity label from the input regions objects through cascading these layers each label can be assigned to the corresponding region s attention is focused on recognizing x ray ct computed tomography images of human heads e g anatomic structure in a medical image the proposed csnn is capable of identifying the components of a brain in a preliminarily segmented image the major components in a human head include bone ventricle and gyrus therefore three layers are needed for this task each layer is constructed based on the principles proposed in kohonen s self organizing feature maps and the optimal linear associative memories and their weights are trained by the features of each entity in the prestored model the experimental results show that the proposed approach is very promising

stabilized finite element methods for the velocity pressure stress formulation of incompressible flows abstract formulated in terms of velocity pressure and the extra stress tensor the incompressible navier stokes equations are discretized by stabilized finite element methods the stabilized methods proposed are analyzed for a linear model and extended to the navier stokes equations the numerical tests performed confirm the good stability characteristics of the methods these methods are applicable to various combinations of interpolation functions including the simplest equal order linear and bilinear elements

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

a taxonomy of consistently stabilized finite element methods for the stokes problem stabilized mixed methods can circumvent the restrictive inf sup condition without introducing penalty errors for properly chosen stabilization parameters these methods are well posed for all conforming velocity pressure pairs however their variational forms have widely varying properties first stabilization offers a choice between weakly or strongly coercive bilinear forms that give rise to linear systems with identical solutions but very different matrix properties second coercivity may be conditional upon a proper choice of a stabilizing parameter here we focus on how these two aspects of stabilized methods affect their accuracy and efficient iterative solution we present results that indicate a preference of krylov subspace solvers for strongly coercive formulations stability criteria obtained by finite element and algebraic analyses are compared with numerical experiments while for two popular classes of stabilized methods sufficient stability bounds correlate well with numerical stability our experiments indicate the intriguing possibility that the pressure stabilized galerkin method is unconditionally stable

reasoning about temporal relations a maximal tractable subclass of allen s interval algebra we introduce a new subclass of allen s interval algebra we call ord horn subclass which is a strict superset of the pointisable subclass we prove that reasoning in the ord horn subclass is a polynomial time problem and show that the path consistency method is sufficient for deciding satisfiability further using an extensive machine generated case analysis we show that the ord horn subclass is a maximal tractable subclass of the full algebra assuming p np in fact it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations

dynamic algorithms for classes of constraint satisfaction problems many fundamental tasks in artificial intelligence and in combinatorial optimization can be formulated as a constraint satisfaction problem csp it is the problem of finding an assignment of values for a set of variables each defined on a finite domain of feasible values subject to a given collection of constraints each constraint is defined over a set of variables and specifies the allowed combinations of values as a collection of tuples in general the problem of finding a solution to a csp is np complete but in some cases it has shown to be polynomially solvable we consider the dynamic version of some polynomially solvable constraint satisfaction problems and present solutions that are better than recomputing everything from scratch after each update the updates we consider are either restrictions i e deletions of values from existing constraints and introduction of new constraints or relaxations i e insertions of values or deletions of constraints

a weak galerkin finite element method for burgers equation abstract we propose a weak galerkin wg finite element method for solving the one dimensional burgers equation based on a new weak variational form both semi discrete and fully discrete wg finite element schemes are established and analyzed we prove the existence of the discrete solution and derive the optimal order error estimates in a discrete h 1 norm and the standard l 2 norm respectively numerical experiments are presented to illustrate our theoretical analysis

variable and value ordering heuristics for the job shop scheduling constraint satisfaction problem abstract practical constraint satisfaction problems csps such as design of integrated circuits or scheduling generally entail large search spaces with hundreds or even thousands of variables each with hundreds or thousands of possible values often only a very tiny fraction of all these possible assignments participates in a satisfactory solution this article discusses techniques that aim at reducing the effective size of the search space to be explored in order to find a satisfactory solution by judiciously selecting the order in which variables are instantiated and the sequence in which possible values are tried for each variable in the csp literature these techniques are commonly referred to as variable and value ordering heuristics our investigation is conducted in the job shop scheduling domain we show that in contrast with problems studied earlier in the csp literature generic variable and value heuristics do not perform well in this domain this is attributed to the difficulty of these heuristics to properly account for the tightness of constraints and or the connectivity of the constraint graphs induced by job shop scheduling csps a new probabilistic framework is introduced that better captures these key aspects of the job shop scheduling search space empirical results show that variable and value ordering heuristics derived within this probabilistic framework often yield significant improvements in search efficiency and significant reductions in the search time required to obtain a satisfactory solution the research reported in this article was the first one along with the work of keng and yun 1989 to use the csp problem solving paradigm to solve job shop scheduling problems the suite of benchmark problems it introduced has been used since then by a number of other researchers to evaluate alternative techniques for the job shop scheduling csp the article briefly reviews some of these more recent efforts and shows that our variable and value ordering heuristics remain quite competitive

the weak galerkin finite element method for the transport reaction equation abstract we present and analyze a weak galerkin finite element method for solving the transport reaction equation in d space dimensions this method is highly flexible by allowing the use of discontinuous finite element on general meshes consisting of arbitrary polygon polyhedra we derive the l 2 error estimate of o h k 1 2 order for the discrete solution when the kth order polynomials are used for k 0 moreover for a special class of meshes we also obtain the optimal error estimate of o h k 1 order in the l 2 norm a derivative recovery formula is presented to approximate the convection directional derivative and the corresponding superconvergence estimate is given numerical examples on compatible and non compatible meshes are provided to show the effectiveness of this weak galerkin method

arc consistency for continuous variables reference lia article 1994 001doi 10 1016 0004 3702 94 90022 1view record in web of science record created on 2006 12 13 modified on 2017 05 12

combining qualitative and quantitative constraints in temporal reasoning abstract this paper presents a general model for temporal reasoning that is capable of handling both qualitative and quantitative information this model allows the representation and processing of many types of constraints discussed in the literature to date including metric constraints restricting the distance between time points and qualitative disjunctive constraints specifying the relative position of temporal objects reasoning tasks in this unified framework are formulated as constraint satisfaction problems and are solved by traditional constraint satisfaction techniques such as backtracking and path consistency new classes of tractable problems are characterized involving qualitative networks augmented by quantitative domain constraints some of which can be solved in polynomial time using arc and path consistency

constraint propogation techniques for the disjunctive scheduling problem abstract constraint propagation is an elementary method for reducing the search space of combinatorial search and optimization problems which has become more and more important in the last decades the basic idea of constraint propagation is to detect and remove inconsistent variable assignments that cannot participate in any feasible solution through the repeated analysis and evaluation of the variables domains and constraints describing a specific problem instance the contribution of this paper is twofold the first contribution is a description of efficient constraint propagation methods also known as consistency tests for the disjunctive scheduling problem dsp which is a generalization of the classical job shop scheduling problem jsp applying an elementary constraint based approach involving a limited number of search variables we will derive consistency tests that ensure 3 b consistency we will further present and analyze both new and classical consistency tests which to some extent are generalizations of the aforementioned consistency tests involving a higher number of variables but still can be implemented efficiently with a polynomial time complexity further the concepts of energetic reasoning and shaving are analyzed and discussed the other contribution is a classification of the consistency tests derived according to the domain reduction achieved the particular strength of using consistency tests is based on their repeated application so that the knowledge derived is propagated i e reused for acquiring additional knowledge the deduction of this knowledge can be described as the computation of a fixed point since this fixed point depends upon the order of the application of the tests we first derive a necessary condition for its uniqueness we then develop a concept of dominance which enables the comparison of different consistency tests as well as a simple method for proving dominance an extensive comparison of all consistency tests is given quite surprisingly we will find out that some apparently stronger consistency tests are subsumed by apparently weaker ones at the same time an open question regarding the effectiveness of energetic reasoning is answered

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

topological parameters for time space tradeoff in this paper we propose a family of algorithms combining tree clustering with conditioning that trade space for time such algorithms are useful for reasoning in probabilistic and deterministic networks as well as for accomplishing optimization tasks by analyzing the problem structure the user can select from a spectrum of algorithms the one that best meets a given time space specification to determine the potential of this approach we analyze the structural properties of problems coming from the circuit diagnosis domain the analysis demonstrates how the tradeoffs associated with various hybrids can be used for each problem instance 2001 elsevier science b v all rights reserved

fugitive search games on graphs and related parameters abstract the goal of a fugitive search game on a graph is to trap a fugitive that hides on the vertices of the graph by systematically placing searchers on the vertices the fugitive is assumed to have complete knowledge of the graph and of the searchers moves but is restricted to move only along paths whose vertices are not guarded by searchers the search number of the graph is the least number of searchers necessary to trap the fugitive variants of the fugitive search game have been related to important graph parameters like treewidth and pathwidth in this paper we introduce a class of fugitive search games where the searchers do not see the fugitive and the fugitive can only move just before a searcher is placed on the vertex it occupies letting the fugitive s speed i e the maximum number of edges the fugitive can traverse at a single move vary we get different games we show that if the speed of the fugitive is unbounded then the search number minus 1 is equal to the treewidth of the graph while if the speed is 1 then the search number minus 1 is equal to a polynomially computable graph parameter which is called width or alternatively linkage and is studied in the context of the constraint satisfaction and boolean satisfiability problems we also show that in the above two cases the search number remains the same even if we consider only search strategies that at every step further restrict the fugitive s possible resorts this monotonicity property is usually expressed as recontamination does not help moreover we give an equivalent characterization of the search number for any given fugitive speed in terms of an elimination ordering of the vertices of the graph using this characterization we show that for any graph if the length of any chordless cycle is bounded by a constant s s 3 then the treewidth of the graph plus 1 is equal to the search number for fugitive speed s 2

the weak galerkin finite element method for the symmetric hyperbolic systems abstract in this paper we present and analyze a weak galerkin finite element wg method for solving the symmetric hyperbolic systems this method is highly flexible by allowing the use of discontinuous finite elements on element and its boundary independently of each other by introducing special weak derivative we construct a stable weak galerkin scheme and derive the optimal l 2 error estimate of o h k 1 2 order for the discrete solution when the k order polynomials are used for k 0 as application we discuss this wg method for solving the singularly perturbed convection diffusion reaction equation and derive an e uniform error estimate of order k 1 2 numerical examples are provided to show the effectiveness of the proposed wg method

the logic of constraint satisfaction the constraint satisfaction problem csp formalization has been a productive tool within artificial intelligence and related areas the finite csp fcsp framework is presented here as a restricted logical calculus within a space of logical representation and reasoning systems fcsp is formulated in a variety of logical settings theorem proving in first order predicate calculus propositional theorem proving and hence sat the prolog and datalog approaches constraint network algorithms a logical interpreter for networks of constraints the constraint logic programming clp paradigm and propositional model finding and hence sat again several standard and some not so standard logical methods can therefore be used to solve these problems by doing this we obtain a specification of the semantics of the common approaches this synthetic treatment also allows algorithms and results from these disparate areas to be imported and specialized to fcsp the special properties of fcsp are exploited to achieve for example completeness and to improve efficiency it also allows export to the related areas by casting csp both as a generalization of fcsp and as a specialization of clp it is observed that some but not all fcsp techniques lift to csp and perhaps thereby to clp various new connections are uncovered in particular between the proof finding approaches and the alternative model finding approaches that have arisen in depiction and diagnosis applications

a stable weak galerkin finite element method for stokes problem abstract we study the weak galerkin finite element method for stokes problem a new weak galerkin finite element velocity pressure space pair is presented which satisfies the discrete inf sup condition based on this space pair we establish a stable weak galerkin approximation scheme without adding any stability term or penalty term then we further derive the optimal error estimates for velocity and pressure approximations respectively numerical experiments are provided to illustrate the theoretical analysis

a weak galerkin mixed finite element method for second order elliptic problems abstract a new weak galerkin wg method is introduced and analyzed for the second order elliptic equation formulated as a system of two first order linear equations this method called wg mfem is designed by using discontinuous piecewise polynomials on finite element partitions with arbitrary shape of polygons polyhedra the wg mfem is capable of providing very accurate numerical approximations for both the primary and flux variables allowing the use of discontinuous approximating functions on arbitrary shape of polygons polyhedra makes the method highly flexible in practical computation optimal order error estimates in both discrete h and l norms are established for the corresponding weak galerkin mixed finite element solutions

combining topological and size information for spatial reasoning information about the size of spatial regions is often easily accessible and when combined with other types of spatial information it can be practically very useful in this paper we introduce four classes of qualitative and metric size constraints and we study their integration with the region connection calculus rcc 8 a well known approach to qualitative spatial reasoning with topological relations we propose a new path consistency algorithm for combining rcc 8 relations and qualitative size relations the algorithm is complete for deciding satisfiability of an input set of topological constraints over one of the three maximal tractable subclasses of rcc 8 containing all the basic relations moreover its time complexity is cubic and is the same as the complexity of the best known method for deciding satisfiability when only these topological relations are considered we also provide results on finding a consistent scenario in cubic time for these combined classes regarding metric size constraints we first study their combination with rcc 8 and we show that deciding satisfiability for the combined sets of constraints is np hard even when only the rcc 8 basic relations are used then we introduce rcc 7 a subalgebra of rcc 8 that can be used for applications where spatial regions cannot partially overlap we show that reasoning with the seven rcc 7 basic relations and the universal relation is intractable but that reasoning with the rcc 7 basic relations combined with metric size information is tractable finally we give a polynomial algorithm for the latter case and a backtracking algorithm for the general case

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

the combinatorics of object recognition in cluttered environments using constrained search abstract the problem of recognizing rigid objects from noisy sensory data has been successfully attacked in previous work by using a constrained search approach empirical investigations have shown the method to be very effective when recognizing and localizing isolated objects but less effective when dealing with occluded objects where much of the sensory data arises from objects other than the one of interest when clustering techniques such as the hough transform are used to isolate likely subspaces of the search space empirical performance in cluttered scenes improves considerably in this note we establish formal bounds on the combinatorics of this approach under some simple assumptions we show that the expected complexity of recognizing isolated objects is quadratic in the number of model and sensory fragments but that the expected complexity of recognizing objects in cluttered environments is exponential in the size of the correct interpretation we also provide formal bounds on the efficacy of using the hough transform to preselect likely subspaces showing that the problem remains exponential but that in practical terms the size of the problem is significantly decreased

arc consistency and arc consistency again abstract there is no need to show the importance of arc consistency in constraint networks mohr and henderson 9 have proposed ac 4 an algorithm with optimal worst case time complexity but it has two drawbacks its space complexity and average time complexity in problems with many solutions where constraints are large these drawbacks become so important that users often replace ac 4 by ac 3 8 a non optimal algorithm in this paper we propose a new algorithm ac 6 which keeps the optimal worst case time complexity of ac 4 while working out the drawback of space complexity moreover the average time complexity of ac 6 is optimal for constraint networks where nothing is known about the constraint semantics

backjump based backtracking for constraint satisfaction problems the performance of backtracking algorithms for solving finite domain constraint satisfaction problems can be improved substantially by look back and look ahead methods look back techniques extract information by analyzing failing search paths that are terminated by dead ends look ahead techniques use constraint propagation algorithms to avoid such dead ends altogether this paper describes a number of look back variants including backjumping and constraint recording which recognize and avoid some unnecessary explorations of the search space the last portion of the paper gives an overview of look ahead methods such as forward checking and dynamic variable ordering and discusses their combination with backjumping

image interpretation with a conceptual graph labeling over segmented images and detection of unexpected objects the labeling of the regions of a segmented image according to a semantic representation ontology is usually associated with the notion of understanding the high combinatorial aspect of this problem can be reduced with local checking of constraints between the elements of the ontology in the classical definition of finite domain constraint satisfaction problem it is assumed that the matching problem between regions and labels is bijective unfortunately in image interpretation the matching problem is often non univocal indeed images are often over segmented one object is made up of several regions this non univocal matching between data and a conceptual graph was not possible until a decisive step was accomplished by the introduction of arc consistency with bilevel constraint fdcsp b c however this extension is only adequate for a matching corresponding to surjective functions in medical image analysis the case of non functional relations is often encountered for example when an unexpected object like a tumor appears in this case the data cannot be mapped to the conceptual graph with a classical approach in this paper we propose an extension of the fdcsp b c to solve the constraint satisfaction problem for non functional relations

empirically derived estimates of the complexity of labeling line drawings of polyhedral scenes abstract several results have been obtained in the past about the complexity of understanding line drawings of polyhedral scenes kirousis and papadimitriou 1988 have shown that the problem of labeling line drawings of trihedral scenes is np complete the human brain however seems to grasp at a glance the 3d structure associated with a line drawing a possible explanation of this discrepancy offered by kirousis and papadimitriou themselves is that the worst case complexity does not reflect the real difficulty of labeling line drawings which might be far less in the average or in typical cases however no statistical analysis has ever been carried out to test this conjecture the core of this paper is an algorithm for the generation of random instances of polyhedral scenes random instances of line drawings are then obtained as perspective projections of these scenes and can be used as an input to standard labeling algorithms so as to derive experimental estimates of the complexity of these algorithms the results indicate that the median case complexity is linear in the number of junctions this substantiates the conjecture that typical instances of line drawings are easy to label and may help explain the ease by which the brain is able to solve the problem

tree clustering for constraint networks research note abstract the paper offers a systematic way of regrouping constraints into hierarchical structures capable of supporting search without backtracking the method involves the formation and preprocessing of an acyclic database that permits a large variety of queries and local perturbations to be processed swiftly either by sequential backtrack free procedures or by distributed constraint propagation processes

backtracking techniques for the job shop scheduling constraint satisfaction problem abstract this paper studies a version of the job shop scheduling problem in which some operations have to be scheduled within non relaxable time windows i e earliest latest possible start time windows this problem is a well known np complete constraint satisfaction problem csp a popular method for solving this type of problems involves using depth first backtrack search in our earlier work we focused on the development of consistency enforcing techniques and variable value ordering heuristics that improve the efficiency of this search procedure in this paper we combine these techniques with new look back schemes that help the search procedure recover from so called deadend search states i e partial solutions that cannot be completed without violating some constraints more specifically we successively describe three intelligent backtracking schemes 1 dynamic consistency enforcement dynamically identifies critical subproblems and determines how far to backtrack by selectively enforcing higher levels of consistency among variables participating in these critical subproblems 2 learning ordering from failure dynamically modifies the order in which variables are instantiated based on earlier conflicts and 3 incomplete backjumping heuristic abandons areas of the search space that appear to require excessive computational efforts these schemes are shown to 1 further reduce the average complexity of the backtrack search procedure 2 enable our system to efficiently solve problems that could not be solved otherwise due to excessive computation cost and 3 be more effective at solving job shop scheduling problems than other look back schemes advocated in the literature

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

a weak galerkin finite element method for second order elliptic problems this paper introduces a finite element method by using a weakly defined gradient operator over generalized functions the use of weak gradients and their approximations results in a new concept called discrete weak gradients which is expected to play an important role in numerical methods for partial differential equations this article intends to provide a general framework for managing differential operators on generalized functions as a demonstrative example the discrete weak gradient operator is employed as a building block in the design of numerical schemes for a second order elliptic problem in which the classical gradient operator is replaced by the discrete weak gradient the resulting numerical scheme is called a weak galerkin wg finite element method it can be seen that the weak galerkin method allows the use of totally discontinuous functions in the finite element procedure for the second order elliptic problem an optimal order error estimate in both a discrete h 1 and l 2 norms are established for the corresponding weak galerkin finite element solutions a superconvergence is also observed for the weak galerkin approximation

the complexity of understanding line drawings of origami scenes this paper deals with the interpretation of line drawings of origami scenes kanade 1980 that is scenes obtained by assembling planar panels of negligible thickness and it addresses the computational complexity of the problem of consistently assigning suitable labels to the segments describing 3d properties as convexity concavity and occlusion labeling problem the main results of the paper are the following a the labeling problem for line drawings of origami scenes is np as for the case of trihedral scenes b the problem remains np even if the location of the vanishing points in the image plane is given whereas for trihedral scenes the problem was polynomially solvable c in case the vanishing points are known the labeling problem can be subdivided into two subproblems the paneling problem and the labeling a paneled line drawing problem which are both polynomially solvable there may be however exponentially many legal panelings to check against labelability

comments on mohr and henderson s path consistency algorithm abstract mohr and henderson have presented new algorithms for arc and path consistency in 1 though the underlying ideas of their algorithms are correct the path consistency algorithm pc 3 is in error in this paper we point out the errors in this algorithm and give a correct one the time complexity and space complexity of the revised algorithm are also analyzed

semiring based constraint satisfaction and optimization we introduce a general framework for constraint satisfaction and optimization where classical csps fuzzy csps weighted csps partial constraint satisfaction and others can be easily cast the framework is based on a semiring structure where the set of the semiring specifies the values to be associated with each tuple of values of the variable domain and the two semiring operations and x model constraint projection and combination respectively local consistency algorithms as usually used for classical csps can be exploited in this general framework as well provided that certain conditions on the semiring operations are satisfied we then show how this framework can be used to model both old and new constraint solving and optimization schemes thus allowing one to both formally justify many informally taken choices in existing schemes and to prove that local consistency techniques can be used also in newly defined schemes

reasoning about qualitative temporal information abstract representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks an interval based framework and a point based framework have been proposed for representing such temporal information in this paper we address two fundamental reasoning tasks that arise in applications of these frameworks given possibly indefinite and incomplete knowledge of the relationships between some intervals or points i find a scenario that is consistent with the information provided and ii find the feasible relations between all pairs of intervals or points for the point based framework and a restricted version of the interval based framework we give computationally efficient procedures for finding a consistent scenario and for finding the feasible relations our algorithms are marked improvements over the previously known algorithms in particular we develop an o n2 time algorithm for finding one consistent scenario that is an o n improvement over the previously known algorithm where n is the number of intervals or points and we develop an algorithm for finding all the feasible relations that is of far more practical use than the previously known algorithm for the unrestricted version of the interval based framework finding a consistent scenario and finding the feasible relations have been shown to be np complete we show how the results for the point algebra aid in the design of a backtracking algorithm for finding one consistent scenario that is shown to be useful in practice for planning problems

a modified weak galerkin finite element method for the stokes equations a modified weak galerkin mwg finite element method is introduced for the stokes equations in the primary velocity pressure formulation this method is based on the weak galerkin wg finite element method developed recently in wang and ye 0000 the unknowns associated with element boundaries in the wg method have been eliminated in the mwg method as the result the mwg method has fewer degrees of freedom optimal order error estimates are established for the corresponding numerical approximation in various norms numerical results are presented to confirm the theory

the upper bound neural network and a class of consistent labeling problems the upper bound neural network ubnn is proposed for solving a class of consistent labeling problems clp crossbar switching is used as an illustration the set of stable attractors of the dynamical system is identically the set of feasible solutions to the problem clp is a general class of np complete neyman pearson problems intersecting artificial intelligence symbolic logic and operations research problems which can be formulated as clp include image segmentation as well as finding spanning trees and euler tours in a graph as an example the ubnn is used to control a crossbar packet switch the switch control problem is a maximal matching problem which is approximated by the ubnn as switching speeds push below the nanosecond range the o v sup 3 time complexity of the maximal matching problem will be prohibitive for large switches when viewed as an analog circuit the ubnn scales well guarantees convergence to a solution of the problem and converges in near constant time thus becoming an alternative for large crossbar switch control

interpreting line drawings of curved objects in this thesis we study the problem of interpreting line drawings of scenes composed or opaque regular solid objects bounded by piecewise smooth surfaces with no markings or texture on them it is assumed that the line drawing has been formed by orthographic projection of such a scene under general viewpoint that the line drawing is error free and that there are no lines due to shadows or specularities our definition implicitly excludes laminae wires and the apices of cones a major component of the interpretation of line drawings is line labelling by line labelling we mean a classification of each image curve as corresponding to either a depth or orientation discontinuity in the scene and b further subclassification of each kind of discontinuity for a depth discontinuity we determine whether it is a limb a locus of points on the surface where the line of sight is tangent to the surface or an occluding edge a tangent plane discontinuity of the surface for an orientation discontinuity we determine whether it corresponds to a convex or concave edge this thesis presents the first mathematically rigorous scheme for labelling line drawings of the class of scenes described by analysing the projection of the neighborhoods of different kinds of points on a piecewise smooth surface we are able to catalog all local labelling possibilities for the different types of junctions in a line drawing an algorithm is developed which utilizes this catalog to determine all legal labellings of the line drawing a local minimum complexity rule at each vertex select those labellings which correspond to the minimum number of faces meeting at the vertex is used in order to prune highly counter intuitive interpretations the labelling scheme was implemented and tested on a number of line drawings the labellings obtained are few and by and large in accordance with human interpretations

on point duration networks for temporal reasoning we present here a point duration network formalism which extends the point algebra model to include additional variables that represent durations between points of time thereafter the new qualitative model is enlarged for allowing unary metric constraints on points and durations subsuming in this way several point based approaches to temporal reasoning we deal with some reasoning tasks within the new models and we show that the main problem deciding consistency is np complete however tractable special cases are identified and we show efficient algorithms for checking consistency finding a solution and obtaining the minimal network

constraint satisfaction from a deductive viewpoint research note abstract this paper reports the result of testing the author s proof techniques on the class of constraint satisfaction problems csps this experiment has been successful in the sense that a completely general proof technique turns out to behave well also for this special class of problems which itself has received considerable attention in the community so at the same time the paper happens to present a new deductive mechanism for solving constraint satisfaction problems that is of interest in its own right this mechanism may be characterized as a bottom up lazy evaluation technique which reduces any such problem to the problem of evaluating a database expression typically involving a number of joins a way of computing such an expression is proposed

a comparative study on the weak galerkin discontinuous galerkin and mixed finite element methods this paper presents a comparative study on the newly introduced weak galerkin finite element methods wgfems with the widely accepted discontinuous galerkin finite element methods dgfems and the classical mixed finite element methods mfems for solving second order elliptic boundary value problems we examine the differences similarities and connection among these methods in scheme formulations implementation strategies accuracy and computational cost the comparison and numerical experiments demonstrate that wgfems are viable alternatives to mfems and hold some advantages over dgfems due to their properties of local conservation normal flux continuity no need for penalty factor and definiteness of discrete linear systems

some examples of square integrable representations of semisimple p adic groups we construct irreducible representations of the hecke algebra of an affine weyl group analogous to kilmoyer s reflection representation corresponding to finite weyl groups and we show that in many cases they correspond to a square integrable representation of a simple p adic group

dynamic across time measurement interpretation abstract incrementally maintaining a qualitative understanding of physical system behavior based on observations is crucial to tasks such as real time control monitoring and diagnosis this paper describes the datmi theory for interpretation tasks the key idea of datmi is to dynamically maintain a concise representation of the space of local and global interpretations across time that are consistent with the observations this representation has two key advantages first a set of possible interpretations is more useful than a single best candidate for many tasks such as conservative monitoring second this representation simplifies switching to alternative interpretations when data are faulty or incomplete domain specific knowledge about state and transition probabilities can be used to suggest the interpretation which is most likely domain specific knowledge about durations of states and paths of states can also be used to further constrain the interpretation space when no consistent interpretation exists faulty data hypotheses are generated and then tested by adjusting the interpretation space the datmi theory has been tested via implementation and we describe its performance on two examples

on the parallel complexity of discrete relaxation in constraint satisfaction networks abstract constraint satisfaction networks have been shown to be a very useful tool for knowledge representation in artificial intelligence applications these networks often utilize local constraint propagation techniques to achieve local consistency consistent labeling in vision such methods have been used extensively in the context of image understanding and interpretation as well as planning natural language analysis and truth maintenance systems in this paper we study the parallel complexity of discrete relaxation one of the most commonly used constraint propagation techniques since the constraint propagation procedures such as discrete relaxation appear to operate locally it has been previously believed that the relaxation approach for achieving local consistency has a natural parallel solution our analysis suggests that a parallel solution is unlikely to improve the known sequential solutions by much specifically we prove that the problem solved by discrete relaxation arc consistency is log space complete for p the class of polynomial time deterministic sequential algorithms intuitively this implies that discrete relaxation is inherently sequential and it is unlikely that we can solve the polynomial time version of the consistent labeling problem in logarithmic time by using only a polynomial number of processors some practical implications of our result are discussed we also provide a two way transformation between and or graphs propositional horn satisfiability and local consistency in constraint networks that allows us to develop optimal linear time algorithms for local consistency in constraint networks

effective solution of qualitative interval constraint problems abstract we present a fast algorithm for solving qualitative interval constraint problems which returns solutions of random problems in less than half a second on average with the hardest problem taking only half a minute on a risc workstation this is a surprising result considering the problem is np complete the fast solution time is attributed to the extraordinary pruning power of the path consistency computation and to the fact that all our randomly generated interval networks of size 14 were found to be inconsistent which is rapidly detected by a path consistency computation while inconsistency is relatively easy to prove our algorithm also solves large consistent networks with 100 edges we conclude that our algorithm suffices for solving qualitative interval constraint problems in practice other conclusions are that path consistency reduces the solution search to an almost linear selection of atomic labels and that path consistency is by itself an excellent consistency heuristic for random networks with fewer than 6 or more than 15 nodes

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

partial constraint satisfaction abstract a constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed in some cases it may be impossible or impractical to solve these problems completely we may seek to partially solve the problem in particular by satisfying a maximal number of constraints standard backtracking and local consistency techniques for solving constraint satisfaction problems can be adapted to cope with and take advantage of the differences between partial and complete constraint satisfaction extensive experimentation on maximal satisfaction problems illuminates the relative and absolute effectiveness of these methods a general model of partial constraint satisfaction is proposed

convergence of a hill climbing genetic algorithm for graph matching abstract this paper presents a convergence analysis for the problem of consistent labelling using genetic search the work builds on a recent empirical study of graph matching where we showed that a bayesian consistency measure could be efficiently optimised using a hybrid genetic search procedure which incorporated a hill climbing step in the present study we return to the algorithm and provide some theoretical justification for its observed convergence behaviour the novelty of the analysis is to demonstrate analytically that the hill climbing step significantly accelerates convergence and that the convergence rate is polynomial in the size of the node set of the graphs being matched