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

scaling behavior of explosive percolation on the square lattice clusters generated by the product rule growth model of achlioptas d souza and spencer on a two dimensional square lattice are shown to obey qualitatively different scaling behavior than standard random growth percolation the threshold with unrestricted bond placement allowing loops is found precisely using several different criteria based on both moments and wrapping probabilities yielding p c 0 526 text 565 ifmmode pm else textpm fi 0 000 text 005 consistent with the recent result of radicchi and fortunato the correlation length exponent ensuremath nu is found to be close to 1 the qualitative difference from regular percolation is shown dramatically in the behavior of the percolation probability p ensuremath infty size of largest cluster of the susceptibility and of the second moment of finite clusters where discontinuities appear at the threshold the critical cluster size distribution does not follow a consistent power law for the range of system sizes we study l ensuremath le 8192 but may approach a power law with ensuremath tau g2 for larger l

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

jamming at zero temperature and zero applied stress the epitome of disorder we have studied how two and three dimensional systems made up of particles interacting with finite range repulsive potentials jam i e develop a yield stress in a disordered state at zero temperature and zero applied stress at low packing fractions phi the system is not jammed and each particle can move without impediment from its neighbors for each configuration there is a unique jamming threshold phi c at which particles can no longer avoid each other and the bulk and shear moduli simultaneously become nonzero the distribution of phi c values becomes narrower as the system size increases so that essentially all configurations jam at the same packing fraction in the thermodynamic limit this packing fraction corresponds to the previously measured value for random close packing in fact our results provide a well defined meaning for random close packing in terms of the fraction of all phase space with inherent structures that jam the jamming threshold point j occurring at zero temperature and applied stress and at the random close packing density has properties reminiscent of an ordinary critical point as point j is approached from higher packing fractions power law scaling is found for the divergence of the first peak in the pair correlation function and in the vanishing of the pressure shear modulus and excess number of overlapping neighbors moreover near point j certain quantities no longer self average suggesting the existence of a length scale that diverges at j however point j also differs from an ordinary critical point the scaling exponents do not depend on dimension but do depend on the interparticle potential finally as point j is approached from high packing fractions the density of vibrational states develops a large excess of low frequency modes indeed at point j the density of states is a constant all the way down to zero frequency all of these results suggest that point j is a point of maximal disorder and may control behavior in its vicinity perhaps even at the glass transition

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

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

generalising submodularity and horn clauses tractable optimization problems defined by tournament pair multimorphisms the submodular function minimization problem sfm is a fundamental problem in combinatorial optimization and several fully combinatorial polynomial time algorithms have recently been discovered to solve this problem the most general versions of these algorithms are able to minimize any submodular function whose domain is a set of tuples over any totally ordered finite set and whose range includes both finite and infinite values in this paper we demonstrate that this general form of sfm is just one example of a much larger class of tractable discrete optimization problems defined by valued constraints these tractable problems are characterized by the fact that their valued constraints have an algebraic property which we call a tournament pair multimorphism this larger tractable class also includes the problem of satisfying a set of horn clauses horn sat as well as various extensions of this problem to larger finite domains

metastability effects in bootstrap percolation bootstrap percolation models or equivalently certain types of cellular automata exhibit interesting finite volume effects these are studied at a rigorous level the authors find that for an initial configuration obtained by placing particles independently with probability p or 2 the density of the bootstrapped final configurations in the sequence of cubes l 2 l 2 d typically undergoes an abrupt transition as l is increased from being close to 0 to the value 1 with l fixed at a large value the mean final density as a function of p changes from 0 to 1 around a value which varies only slowly with l the pertinent parameter being lambda p1 d 1 ln l the driving mechanism is the capture of a critical droplet this behaviour is analogous to the decay of a metastable state near a first order phase transition for which the analysis offers some suggestive ideas

probabilistic bootstrap percolation in bootstrap percolation sites are occupied with probabilityp but those with less thanm occupied first neighbors are removed this culling process is repeated until a stable configuration all occupied sites have at leastm occupied first neighbors or the whole lattice is empty is achieved form m 1 the transition is first order while form m 1 it is second order withm dependent exponents in probabilistic bootstrap percolation sites have probabilityr or 1 r of beingm orm sites respectively m sites are those which need at leastm occupied first neighbors to remain occupied we have studied the model on bethe lattices where an exact solution is available form 2 andm 3 the transition changes from second to first order atr 1 1 2 and the exponent is different forr 1 2 the same qualitative behavior is found form 1 andm 3 on the other hand form 1 andm 2 the transition is always second order with the same exponents ofm 1 for any value ofr 0 we found form z 1 andm z wherez is the coordination number of the lattice thatp c 1 for a value ofr which depends onz but is always above zero finally we argue that for bootstrap percolation on real lattices the exponents and form 2 andm 1 are equal for dimensions below 6

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

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

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

a new route to explosive percolation abstract the biased link occupation rule in the achlioptas process ap discourages the large clusters from growing much ahead of others and encourages faster growth of clusters which lag behind in this paper we propose a model where this tendency is sharply reflected in the gamma distribution of the cluster sizes unlike the power law distribution in ap in this model single edges between pairs of clusters of sizes s i and s j are occupied with a probability s i s j the parameter is continuously tunable over the entire real axis numerical studies indicate that for c the transition is first order c 0 for a square lattice and c 1 2 for random graphs in the limits of this model coincides with models well established in the literature

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

arc and path consistence revisited mackworth and freuder have analyzed the time complexity of several constraint satisfaction algorithms 5 we present here new algorithms for arc and path consistency and show that the arc consistency algorithm is optimal in time complexity and of the same order space complexity as the earlier algorithms a refined solution for the path consistency problem is proposed however the space complexity of the path consistency algorithm makes it practicable only for small problems these algorithms are the result of the synthesis techniques used in image a general constraint satisfaction system and local consistency methods 3

1 d expansion for k core percolation the physics of k core percolation pertains to those systems whose constituents require a minimum number of k connections to each other in order to participate in any clustering phenomenon examples of such a phenomenon range from orientational ordering in solid ortho para mathrm h 2 mixtures to the onset of rigidity in bar joint networks to dynamical arrest in glass forming liquids unlike ordinary k 1 and biconnected k 2 percolation the mean field k ensuremath geqslant 3 core percolation transition is both continuous and discontinuous i e there is a jump in the order parameter accompanied with a diverging length scale to determine whether or not this hybrid transition survives in finite dimensions we present a 1 d expansion for k core percolation on the d dimensional hypercubic lattice we show that to order 1 d 3 the singularity in the order parameter and in the susceptibility occur at the same value of the occupation probability this result suggests that the unusual hybrid nature of the mean field k core transition survives in high dimensions

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

reduction operations in fuzzy or valued constraint satisfaction in the constraint satisfaction problem csp knowledge about a relation on n variables is given in the form of constraints on subsets of the variables a solution to the csp is simply an instantiation of the n variables which satisfies all the constraints the fuzzy constraint satisfaction problem fcsp is a generalisation of the csp to the case in which the constraints are not categorical but represent preferences in the form of fuzzy sets the fcsp is then an optimisation problem in the space of all possible instantiations of the n variables it has potentially many more applications in real world problems than the csp when the aim is to maximise the value of the most violated constraint then the fcsp can be solved by solving a logarithmic number of csps fuzzy k consistency can even be established by an algorithm whose worst case complexity is identical to that of an optimal k consistency algorithm for csps when the operator used to aggregate constraint values is strictly monotonic as is the case in max csp for example the classic operation of arc consistency has to be completely redefined we show that an ordered version of arc consistency exists for all fcsps with a strictly monotonic aggregation operator and that in the case of max csp it can be established by an algorithm whose worst case complexity is identical to that of the optimal arc consistency algorithm for csps neighbourhood substitution in csps can be generalised to fuzzy neighbourhood substitution in fcsps whether the aggregation operator is strictly monotonic or idempotent we give an algorithm for applying fuzzy neighbourhood substitutions until convergence based on the corresponding algorithm for csps

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

an optimal k consistency algorithm abstract this paper generalizes the arc consistency algorithm of mohr and henderson 4 and the path consistency algorithm of han and lee 2 to a k consistency algorithm arc consistency and path consistency being 2 consistency and 3 consistency respectively the algorithm is a development of freuder s synthesis algorithm 1 it simultaneously establishes i consistency for each 1 i k it has worst case time and space complexity which is optimal when k is a constant and almost optimal for all other values of k in the case that all order i constraints exist for all 1 i n this algorithm is a solution to the consistent labeling problem with almost optimal worst case time and space complexity

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

cluster aggregation model for discontinuous percolation transitions the evolution of the erd ifmmode mbox h o else h o fi s r enyi er network by adding edges is a basis model for irreversible kinetic aggregation phenomena such er processes can be described by a rate equation for the evolution of the cluster size distribution with the connection kernel k ij ensuremath sim ij where ij is the product of the sizes of two merging clusters here we study that when the giant cluster is discouraged to develop by a sublinear kernel k ij ensuremath sim ij ensuremath omega with 0 ensuremath le ensuremath omega l1 2 the percolation transition pt is discontinuous such discontinuous pt can occur even when the er dynamics evolves from proper initial conditions the obtained evolutionary properties of the simple model sheds light on the origin of the discontinuous pt in other nonequilibrium kinetic systems

on the study of jamming percolation we investigate kinetically constrained models of glassy transitions and determine which model characteristics are crucial in allowing a rigorous proof that such models have discontinuous transitions with faster than power law diverging length and time scales the models we investigate have constraints similar to that of the knights model introduced by toninelli biroli and fisher tbf but differing neighbor relations we find that such knights like models otherwise known as models of jamming percolation need a no parallel crossing rule for the tbf proof of a glassy transition to be valid furthermore most knights like models fail a no perpendicular crossing requirement and thus need modification to be made rigorous we also show how the no parallel crossing requirement can be used to evaluate the provable glassiness of other correlated percolation models by looking at models with more stable directions than the knights model finally we show that the tbf proof does not generalize in any straightforward fashion for three dimensional versions of the knights like models

force balance percolation we study models of correlated percolation where there are constraints on the occupation of sites that mimic force balance i e for a site to be stable requires occupied neighboring sites in all four compass directions in two dimensions we prove rigorously that p c 1 for the two dimensional models studied numerical data indicate that the force balance percolation transition is discontinuous with a growing crossover length with perhaps the same form as the jamming percolation models suggesting that all models belong to the same universality class with the same underlying mechanism driving the transition in both cases we find a lower bound for the correlation length in the connected phase and that the correlation function does not appear to be a power law at the transition finally we study the dynamics of the culling procedure invoked to obtain the force balance configurations and find a dynamical exponent similar to that found in sandpile models

unstable supercritical discontinuous percolation transitions percolation is a pervasive concept 1 which has applications in a wide variety of natural technological and social systems 2 3 4 5 ranging from conductivity of composite materials 6 7 and polymerization 8 to epidemic spreading 9 10 11 and information diffusion 12 13

fundamental properties of neighbourhood substitution in constraint satisfaction problems in combinatorial problems it is often worthwhile simplifying the problem using operations such as consistency before embarking on an exhaustive search for solutions neighbourhood substitution is such a simplification operation whenever a value x for a variable is such that it can be replaced in all constraints by another value y then x is eliminated this paper shows that neighbourhood substitutions are important whether the aim is to find one or all solutions it is proved that the result of a convergent sequence of neighbourhood substitutions is invariant modulo isomorphism an efficient algorithm is given to find such a sequence it is also shown that to combine consistency of any order and neighbourhood substitution we only need to establish consistency once

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

new algorithms for designing unimodular sequences with good correlation properties unimodular i e constant modulus sequences with good autocorrelation properties are useful in several areas including communications and radar the integrated sidelobe level isl of the correlation function is often used to express the goodness of the correlation properties of a given sequence in this paper we present several cyclic algorithms for the local minimization of isl related metrics these cyclic algorithms can be initialized with a good existing sequence such as a golomb sequence a frank sequence or even a pseudo random sequence to illustrate the performance of the proposed algorithms we present a number of examples including the design of sequences that have virtually zero autocorrelation sidelobes in a specified lag interval and of long sequences that could hardly be handled by means of other algorithms previously suggested in the literature

complementary sequences for isi channel estimation a merit factor based on the sequence autocorrelation function whose minimization leads to the reduction in the cramer rao lower bound crlb for the variance of two sided intersymbol interference isi channel estimation is introduced pairs of binary pilot symbol sequences a preamble and a postamble for channel estimation are jointly designed to minimize this merit factor given that the number of channel taps is l and the length of a pilot symbol sequence is n l 1 where n spl ges l we distinguish between the case when n is even and the case when it is odd for even n we show that complementary sequences not only minimize the merit factor but also the crlb for a subset of odd n we construct almost complementary periodic sequence pairs that minimize the merit factor the optimal pilot symbol block signaling requires alternating between two in most cases different binary sequences that form the merit minimizing pair

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

cyclic consistency a local reduction operation for binary valued constraints valued constraint satisfaction provides a general framework for optimisation problems over finite domains it is a generalisation of crisp constraint satisfaction allowing the user to express preferences between solutions consistency is undoubtedly the most important tool for solving crisp constraints it is not only a family of simplification operations on problem instances it also lies at the heart of intelligent search techniques g kondrak p van beek artificial intelligence 89 1997 365 387 and provides the key to solving certain classes of tractable constraints p g jeavons d a cohen m c cooper artificial intelligence 101 1998 251 265 arc consistency was generalised to valued constraints by sacrificing the uniqueness of the arc consistency closure m c cooper t schiex artificial intelligence in press the notion of 3 cyclic consistency introduced in this paper again sacrifices the unique closure property in order to obtain a generalisation of path consistency to valued constraints which is checkable in polynomial time in max csp 3 cyclic consistency can be established in polynomial time and even guarantees a local form of optimality the space complexity of 3 cyclic consistency is optimal since it creates no new constraints

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

correlated percolation and tricriticality the recent proliferation of correlated percolation models models where the addition of edges and or vertices is no longer independent of other edges and or vertices has been motivated by the quest to find discontinuous percolation transitions the leader in this proliferation is what is known as explosive percolation a recent proof demonstrates that a large class of explosive percolation type models does not in fact exhibit a discontinuous transition riordan and warnke science 333 322 2011 here we discuss two lesser known correlated percolation models the k 3 core model on random graphs and the counter balance model in two dimensions both exhibiting discontinuous transitions to search for tricriticality we construct mixtures of these models with other percolation models exhibiting the more typical continuous transition using a powerful rate equation approach we demonstrate that a mixture of k 2 core and k 3 core vertices on the random graph exhibits a tricritical point however for a mixture of k core and counter balance vertices in two dimensions as the fraction of counter balance vertices is increased numerics and heuristic arguments suggest that there is a line of continuous transitions with the line ending at a discontinuous transition i e when all vertices are counter balanced interestingly these heuristic arguments may help identify the ingredients needed for a discontinuous transition in low dimensions in addition our results may have potential implications for glassy and jamming systems

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

complex optimal sequences with constant magnitude for fast channel estimation initialization optimal sounding sequences which satisfy a certain autocorrelation property are useful for fast channel estimation techniques which are based on noniterative channel sounding methods we study optimal sequences consisting of complex symbols with constant magnitude an indirect sequence construction method is derived by considering the phase difference between sequence symbols our construction method includes periodic and nonperiodic optimal sequences and provides insight into the nature and properties of optimal sequences that are based on consecutive roots of unity phase difference sequences

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

the complexity of 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

ml estimation of time and frequency offset in ofdm systems we present the joint maximum likelihood ml symbol time and carrier frequency offset estimator in orthogonal frequency division multiplexing ofdm systems redundant information contained within the cyclic prefix enables this estimation without additional pilots simulations show that the frequency estimator may be used in a tracking mode and the time estimator in an acquisition mode

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

synthesizing low autocorrelation and low papr ofdm sequences under spectral constraints through convex optimization and gs algorithm sequences with low autocorrelation ac and low peak to average power ratio papr are desired in many communication or signal processing applications this work investigates the synthesis of ofdm sequences with the desired low ac and low papr under spectral constraints the spectral constraints limit the maximum allowable power on each subcarrier to avoid interference on particular reserved bands and undesirable dc offset the first part of this work discusses the design of sequences with periodic ac property under spectral constraints specifically we present a convex optimization method for synthesizing ofdm sequences with minimized peak sidelobe level psl or weighted sum of sidelobe levels wssl of the periodic ac function within specified time lags the design objective to be minimized can also be a certain convex function of the sequence ac sidelobes furthermore we present methods based on gerchberg saxton gs algorithm to decrease the papr of the sequences while maintaining the optimized ac characteristic the second part of this work investigates the aperiodic ac under spectral constraints in this case the optimal sequence design problem is nonconvex by relaxing the nonconvex problem to a convex problem we provide lower bounds for psl and wssl of the aperiodic ac function based on the optimal solution for the relaxed convex problem we present an efficient algorithm to find sequences with low papr and near optimal aperiodic ac property while the spectral constraints are satisfied

multiple access interference reduction for qs cdma systems with a novel class of polyphase sequences in this paper a new class of polyphase sequences for cdma systems and its generation method are suggested and the correlation properties of the sequence are investigated the performance of the sequence in quasi synchronous cdma qs cdma systems is investigated under a frequency selective time nonselective slow nakagami fading channel with additive white gaussian noise awgn it is shown that the performance of the qs cdma systems using the suggested sequence is independent of the number of users and is much better than that using the pn sequence

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

explosive percolation a numerical analysis percolation is one of the most studied processes in statistical physics a recent paper by achlioptas et al science 323 1453 2009 showed that the percolation transition which is usually continuous becomes discontinuous explosive if links are added to the system according to special cooperative rules achlioptas processes in this paper we present a detailed numerical analysis of achlioptas processes with product rule on various systems including lattices random networks a la erdos renyi and scale free networks in all cases we recover the explosive transition by achlioptas et al however the explosive percolation transition is kind of hybrid as despite the discontinuity of the order parameter at the threshold one observes traces of analytical behavior such as power law distributions of cluster sizes in particular for scale free networks with degree exponent 3 all relevant percolation variables display power law scaling just as in continuous second order phase transitions

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

multi agent oriented constraint satisfaction this paper presents a multi agent oriented method for solving csps constraint satisfaction problems in this method distributed agents represent variables and a two dimensional grid like environment in which the agents inhabit corresponds to the domains of the variables thus the positions of the agents in such an environment constitute the solution to a csp in order to reach a solution state the agents will rely on predefined local reactive behaviors namely better move least move and random move while presenting the formalisms and algorithm we will analyze the correctness and complexity of the algorithm and demonstrate the proposed method with two benchmark csps i e n queen problems and coloring problems in order to further determine the effectiveness of different reactive behaviors we will examine the performance of this method in deriving solutions based on behavior prioritization and different selection probabilities

universality in bootstrap and diffusion percolation critical concentrations and exponents of bootstrap and diffusion site percolation models are presented for the triangular lattice results are based on numerical simulations and are consistent with universal exponents for random bootstrap and diffusion percolation

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