consistent labeling problems and their algorithms expected complexities and theory based heuristics a new parameter is introduced to characterize a type of search problem of broad relevance in artificial intelligence operations research and symbolic logic this parameter which we call inter variable compatibility is particularly important in that complexity analyses incorporating it are able to capture the dependence of problem complexity on search order used by an algorithm thus compatibility based theories can provide a theoretical basis for the extraction of heuristics for choosing good search orderings a long sought goal for such problems since it can lead to significant savings during search we carry out expected complexity analyses for the traditional backtrack algorithm as well as for two more recent algorithms that have been found empirically to be significant improvements forward checking and word wise forward checking we extract compatibility based ordering heuristics from the theory for forward checking preliminary experimental results are presented showing the large savings that result from their use similar savings can be expected for other algorithms when heuristics taking account of inter variable compatibilities are used our compatibility based theories also provide a more precise way of predicting which algorithm is best for a given problem

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

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

direct evaluation of large deviation functions we introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities such as current or density that are local in time the large deviation functions are given in terms of the typical properties of a modified dynamics and since they no longer involve rare events can be evaluated efficiently and over a wider ranges of values we illustrate the method with the current fluctuations of the totally asymmetric exclusion process and with the work distribution of a driven lorentz gas

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

semi infinite programming theory methods and applications starting from a number of motivating and abundant applications in 2 including control of robots eigenvalue computations mechanical stress of materials and statistical design the authors describe a class of optimization problems which are referred to as semi infinite because their constraints bound functions of a finite number of variables on a whole region in 3 5 first and second order optimality conditions are derived for general nonlinear problems as well as a procedure for reducing the problem locally to one with only finitely many constraints another main effort for achieving simplification is through duality in 6 there algebraic properties of finite linear programming are brought to bear on duality theory in semi infinite programming section 7 treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent sqp type methods taking this differentiable point of view this paper can be considered to be complementar

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

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

an unconstrained convex programming approach to linear semi infinite programming in this paper an unconstrained convex programming dual approach for solving a class of linear semi infinite programming problems is proposed both primal and dual convergence results are established under some basic assumptions numerical examples are also included to illustrate this approach

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

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

cover time for random walks on arbitrary complex networks we present an analytical method for computing the mean cover time of a discrete time random walk process on arbitrary complex networks the cover time is defined as the time a random walker requires to visit every node in the network at least once this quantity is particularly important for random search processes and target localization on network structures based on the global mean first passage time of target nodes we derive a method for computing the cumulative distribution function of the cover time based on first passage time statistics our method is viable for networks on which random walks equilibrate quickly we show that it can be applied successfully to various model and real world networks our results reveal an intimate link between first passage and cover time statistics and offer a computationally efficient way for estimating cover times in network related applications

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

entropy rate of diffusion processes on complex networks we introduce the concept of entropy rate to characterize a diffusion process on a complex network the entropy rate represents the minimal amount of information necessary to describe the diffusion on the network and is a quantity extremely sensitive to the network topology and dynamics by opportunely tuning the kind of diffusion the entropy rate allows one to extract different properties of the network structure moreover entropy maximization indicates how to design optimal diffusion processes providing a new theoretical tool with applications to social technological and communication systems

disease extinction in the presence of random vaccination we investigate disease extinction in an epidemic model described by a birth death process we show that in the absence of vaccination the effective entropic barrier for extinction displays scaling with the distance to the bifurcation point with an unusual critical exponent even a comparatively weak poisson distributed random vaccination leads to an exponential increase in the extinction rate with the exponent that strongly depends on the vaccination parameters

large deviations of the current for driven periodic diffusions we study the large deviations of the time integrated current for a driven diffusion on the circle often used as a model of nonequilibrium systems we obtain the large deviation functions describing the current fluctuations using a fourier bloch decomposition of the so called tilted generator and we also construct from this decomposition the effective biased auxiliary or driven markov process describing the diffusion as current fluctuations are observed in time this effective process provides a clear physical explanation of the various fluctuation regimes observed it is used here to obtain an upper bound on the current large deviation function which we compare to a recently derived entropic bound and to study the low noise limit of large deviations

manipulation of extreme events on scale free networks extreme events taking place on networks are not uncommon we show that it is possible to manipulate the extreme event occurrence probabilities and distribution over the nodes of a scale free network by tuning the nodal capacity this can be used to reduce the number of extreme event occurrences however monotonic nodal capacity enhancements beyond a point do not lead to any substantial reduction in the number of extreme events we point out the practical implication of this result for network design in the context of reducing extreme event occurrences

efficient algorithm for solving semi infinite programming problems and their applications to nonuniform filter bank designs an efficient algorithm for solving semi infinite programming problems is proposed in this paper the index set is constructed by adding only one of the most violated points in a refined set of grid points by applying this algorithm for solving the optimum nonuniform symmetric antisymmetric linear phase finite impulse response fir filter bank design problems the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorithm

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

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

revealing the microstructure of the giant component in random graph ensembles the microstructure of the giant component of the erd s renyi network and other configuration model networks is analyzed using generating function methods while configuration model networks are uncorrelated the giant component exhibits a degree distribution which is different from the overall degree distribution of the network and includes degree degree correlations of all orders we present exact analytical results for the degree distributions as well as higher order degree degree correlations on the giant components of configuration model networks we show that the degree degree correlations are essential for the integrity of the giant component in the sense that the degree distribution alone cannot guarantee that it will consist of a single connected component to demonstrate the importance and broad applicability of these results we apply them to the study of the distribution of shortest path lengths on the giant component percolation on the giant component and spectra of sparse matrices defined on the giant component we show that by using the degree distribution on the giant component one obtains high quality results for these properties which can be further improved by taking the degree degree correlations into account this suggests that many existing methods currently used for the analysis of the whole network can be adapted in a straightforward fashion to yield results conditioned on the giant component

convergence of large deviation estimators we study the convergence of statistical estimators used in the estimation of large deviation functions describing the fluctuations of equilibrium nonequilibrium and manmade stochastic systems we give conditions for the convergence of these estimators with sample size based on the boundedness or unboundedness of the quantity sampled and discuss how statistical errors should be defined in different parts of the convergence region our results shed light on previous reports of phase transitions in the statistics of free energy estimators and establish a general framework for reliably estimating large deviation functions from simulation and experimental data and identifying parameter regions where this estimation converges

rare events and discontinuous percolation transitions percolation theory characterizing the robustness of a network has applications ranging from biology to epidemic spreading and complex infrastructures percolation theory however only concerns the average response of a network to random damage of its nodes while in real finite networks fluctuations around this average behavior are observable consequently for finite networks there is an urgent need to evaluate the risk of collapse in response to rare configurations of the initial damage here we build a large deviation theory of percolation characterizing the response of a sparse network to rare events this general theory includes the second order phase transition observed typically for random configurations of the initial damage but reveals also discontinuous transitions corresponding to rare configurations of the initial damage for which the size of the giant component is suppressed

linear semi infinite programming theory an updated survey abstract this paper presents an state of the art survey on linear semi infinite programming theory and its extensions in particular convex semi infinite programming this review updates a previous survey semi infinite programming non convex optim appl 25 1998 of the same authors on the same topic which was published in 1998

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

solving convex programs with infinitely many linear constraints by a relaxed cutting plane method abstract one of the major computational bottlenecks of using the conventional cutting plane approach to solve convex programming problems with infinitely many linear constraints lies in finding a global optimizer of a nonlinear and nonconvex program this paper presents a relaxed scheme to generate a new cut in each iteration the proposed scheme chooses a point at which the constraints are violated to a degree rather than at which the violation is maximized a convergence proof is provided the proposed scheme also exhibits the capability of generating an approximate solution to any level of accuracy in a finite number of iterations

diffusions conditioned on occupation measures a markov process fluctuating away from its typical behavior can be represented in the long time limit by another markov process called the effective or driven process having the same stationary states as the original process conditioned on the fluctuation observed we construct here this driven process for diffusions spending an atypical fraction of their evolution in some region of state space corresponding mathematically to stochastic differential equations conditioned on occupation measures as an illustration we consider the langevin equation conditioned on staying for a fraction of time in different intervals of the real line including the positive half line which leads to a generalization of the brownian meander problem other applications related to quasi stationary distributions metastable states noisy chemical reactions queues and random walks are discussed

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

epidemic extinction paths in complex networks we study the extinction of long lived epidemics on finite complex networks induced by intrinsic noise applying analytical techniques to the stochastic susceptible infected susceptible model we predict the distribution of large fluctuations the most probable or optimal path through a network that leads to a disease free state from an endemic state and the average extinction time in general configurations our predictions agree with monte carlo simulations on several networks including synthetic weighted and degree distributed networks with degree correlations and an empirical high school contact network in addition our approach quantifies characteristic scaling patterns for the optimal path and distribution of large fluctuations both near and away from the epidemic threshold in networks with heterogeneous eigenvector centrality and degree distributions

large deviations of random walks on random graphs we study the rare fluctuations or large deviations of time integrated functionals or observables of an unbiased random walk evolving on erdos renyi random graphs and construct a modified biased random walk that explains how these fluctuations arise in the long time limit two observables are considered the sum of the degrees visited by the random walk and the sum of their logarithm related to the trajectory entropy the modified random walk is used for both quantities to explain how sudden changes in degree fluctuations similar to dynamical phase transitions are related to localization transitions for the second quantity we also establish links between the large deviations of the trajectory entropy and the maximum entropy random walk

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

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

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

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

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

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

maximal entropy random walks in complex networks with limited information maximization of the entropy rate is an important issue to design diffusion processes aiming at a well mixed state we demonstrate that it is possible to construct maximal entropy random walks with only local information on the graph structure in particular we show that an almost maximal entropy random walk is obtained when the step probabilities are proportional to a power of the degree of the target node with an exponent that depends on the degree degree correlations and is equal to 1 in uncorrelated graphs

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

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