Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into that intractability and help identify special cases in which symmetry can be dealt with more tractably.
The study of computational complexity in constraint programming has tended to focus on the structure of the constraint graph (e.g. especially measures like tree width @cite_33 @cite_42 ) or on the semantics of the constraints (e.g. @cite_4 ). However, these lines of research are mostly concerned with constraint satisfaction problems as a whole, and do not say much about individual (global) constraints. For global constraints of bounded arity, asymptotic analysis has been used to characterize the complexity of propagation both in general and for constraints with a particular semantics. For example, the generic domain consistency algorithm of @cite_39 has an @math time complexity on constraints of arity @math and domains of size @math , whilst the domain consistency algorithm of @cite_5 for the @math -ary constraint has @math time complexity. Bessiere showed that many global constraints like are also intractable to propagate @cite_36 . More recently, Samer and Szeider have studied the parameterized complexity of the constraint @cite_19 . Szeider has also studied the complexity of symmetry in a propositional resolution calculus @cite_25 . See Chapter 10 in @cite_8 for more about symmetry of propositional systems.
@cite_4 @cite_33 @cite_8 @cite_36 @cite_42 @cite_39 @cite_19 @cite_5 @cite_25
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We study the computational complexity of reasoning with global constraints. We show that reasoning with such constraints is intractable in general. We then demonstrate how the same tools of computational complexity can be used in the design and analysis of specific global constraints. In particular, we illustrate how computational complexity can be used to determine when a lesser level of local consistency should be enforced, when decomposing constraints will lose pruning, and when combining constraints is tractable. We also show how the same tools can be used to study symmetry breaking, meta-constraints like the cardinality constraint, and learning nogoods. The valued constraint satisfaction problem (VCSP) is an optimization framework originating from artificial intelligence which generalizes the classical constraint satisfaction problem (CSP). In this paper, we are interested in structural properties that can make problems from the VCSP framework, as well as other CSP variants, solvable to optimality in polynomial time. So far, the largest structural class that is known to be polynomial-time solvable to optimality is the class of bounded hypertree width instances introduced by Here, larger classes of tractable instances are singled out by using dynamic programming and structural decompositions based on a hypergraph invariant proposed by Grohe and Marx. In the second part of the paper, we take a different view on our optimization problems; instead of considering fixed arbitrary values for some structural invariant of the (hyper)graph structure of the constraints, we consider the problems parameterized by the tree-width of primal, dual, and incidence graphs, combined with several other basic parameters such as domain size and arity. Such parameterizations of plain CSPs have been studied by Samer and Szeider. Here, we extend their framework to encompass our optimization problems, by coupling it with further non-trivial machinery and new reductions. By doing so, we are able to determine numerous combinations of the considered parameters that make our optimization problems admit fixed-parameter algorithms. We show that tools from circuit complexity can be used to study decompositions of global constraints. In particular, we study decompositions of global constraints into conjunctive normal form with the property that unit propagation on the decomposition enforces the same level of consistency as a specialized propagation algorithm. We prove that a constraint propagator has a a polynomial size decomposition if and only if it can be computed by a polynomial size monotone Boolean circuit. Lower bounds on the size of monotone Boolean circuits thus translate to lower bounds on the size of decompositions of global constraints. For instance, we prove that there is no polynomial sized decomposition of the domain consistency propagator for the ALLDIFFERENT constraint. We study the consistency and domain consistency problem for extended global cardinality (EGC) constraints. An EGC constraint consists of a set X of variables, a set D of values, a domain @math for each variable x, and a "cardinality set" K(d) of non-negative integers for each value d. The problem is to instantiate each variable x with a value in D(x) such that for each value d, the number of variables instantiated with d belongs to the cardinality set K(d). It is known that this problem is NP-complete in general, but solvable in polynomial time if all cardinality sets are intervals. First we pinpoint connections between EGC constraints and general factors in graphs. This allows us to extend the known polynomial-time case to certain non-interval cardinality sets. Second we consider EGC constraints under restrictions in terms of the treewidth of the value graph (the bipartite graph representing variable-value pairs) and the cardinality-width (the largest integer occurring in the cardinality sets). We show that EGC constraints can be solved in polynomial time for instances of bounded treewidth, where the order of the polynomial depends on the treewidth. We show that (subject to the complexity theoretic assumption FPT???W[1]) this dependency cannot be avoided without imposing additional restrictions. If, however, also the cardinality-width is bounded, this dependency gets removed and EGC constraints can be solved in linear time. For certain subclasses of NP, @math P, or #P characterized by local constraints, it is known that if there exist any problems within that subclass that are not polynomial time computable, then all the problems in the subclass are NP-complete, @math P-complete, or #P-complete. Such dichotomy results have been proved for characterizations such as constraint satisfaction problems and directed and undirected graph homomorphism problems, often with additional restrictions. Here we give a dichotomy result for the more expressive framework of Holant problems. For example, these additionally allow for the expression of matching problems, which have had pivotal roles in the development of complexity theory. As our main result we prove the dichotomy theorem that, for the class @math P, every set of symmetric Holant signatures of any arities that is not polynomial time computable is @math P-complete. The result exploits some special properties of the class @math P and characterizes four distinct tractable ... We investigate the computational complexity of two global constraints, CUMULATIVE and INTERDISTANCE. These are key constraints in modeling and solving scheduling problems. Enforcing domain consistency on both is NP-hard. However, restricted versions of these constraints are often sufficient in practice. Some examples include scheduling problems with a large number of similar tasks, or tasks sparsely distributed over time. Another example is runway sequencing problems in air-traffic control, where landing periods have a regular pattern. Such cases can be characterized in terms of structural restrictions on the constraints. We identify a number of such structural restrictions and investigate how they impact the computational complexity of propagating these global constraints. In particular, we prove that such restrictions often make propagation tractable. We propose AllDiffPrecedence, a new global constraint that combines together an AllDifferent constraint with precedence constraints that strictly order given pairs of variables. We identify a number of applications for this global constraint including instruction scheduling and symmetry breaking. We give an efficient propagation algorithm that enforces bounds consistency on this global constraint. We show how to implement this propagator using a decomposition that extends the bounds consistency enforcing decomposition proposed for the AllDifferent constraint. Finally, we prove that enforcing domain consistency on this global constraint is NP-hard in general. We revisit the SeqBin constraint. This meta-constraint subsumes a number of important global constraints like Change, Smooth and IncreasingNValue. We show that the previously proposed filtering algorithm for SeqBin has two drawbacks even under strong restrictions: it does not detect bounds disentailment and it is not idempotent. We identify the cause for these problems, and propose a new propagator that overcomes both issues. Our algorithm is based on a connection to the problem of finding a path of a given cost in a restricted @math -partite graph. Our propagator enforces domain consistency in O(nd^2) and, for special cases of SeqBin that include Change, Smooth and IncreasingNValue, in O(nd) time. We study from a formal perspective the consistency and propagation of constraints involving multiset variables. That is, variables whose values are multisets. These help us model problems more naturally and can, for example, prevent introducing unnecessary symmetry into a model. We identify a number of different representations for multiset variables and compare them. We then propose a definition of local consistency for constraints involving multiset, set and integer variables. This definition is a generalization of the notion of bounds consistency for integer variables. We show how this local consistency property can be enforced by means of some simple inference rules which tighten bounds on the variables. We also study a number of global constraints on set and multiset variables. Surprisingly, unlike finite domain variables, the decomposition of global constraints over set or multiset variables often does not hinder constraint propagation. We propose a new family of constraints which combine together lexicographical ordering constraints for symmetry breaking with other common global constraints. We give a general purpose propagator for this family of constraints, and show how to improve its complexity by exploiting properties of the included global constraints. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . We describe the design and implementation of a finite domain constraint solver embedded in a Prolog system using an extended unification mechanism via attributed variables as a generic constraint interface. The solver is essentially a scheduler for indexicals, i.e. reactive functional rules encoding local consistency methods performing incremental constraint solving or entailment checking, and global constraints, i.e. general propagators which may use specialized algorithms to achieve a higher degree of consistency or better time and space complexity. Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... The old Asian legend about the blind men and the elephant comes to mind when looking at how different authors of scientific papers describe a piece of related prior work. It turns out that different citations to the same paper often focus on different aspects of that paper and that neither provides a full description of its full set of contributions. In this article, we will describe our investigation of this phenomenon. We studied citation summaries in the context of research papers in the biomedical domain. A citation summary is the set of citing sentences for a given article and can be used as a surrogate for the actual article in a variety of scenarios. It contains information that was deemed by peers to be important. Our study shows that citation summaries overlap to some extent with the abstracts of the papers and that they also differ from them in that they focus on different aspects of these papers than do the abstracts. In addition to this, co-cited articles (which are pairs of articles cited by another article) tend to be similar. We show results based on a lexical similarity metric called cohesion to justify our claims. © 2008 Wiley Periodicals, Inc. Statistical physics models with hard constraints, such as the discrete hard-core gas model (random independent sets in a graph), are inherently combinatorial and present the discrete mathematician with a relatively comfortable setting for the study of phase transition. In this paper we survey recent work (concentrating on joint work of the authors) in which hard-constraint systems are modeled by the space @math of homomorphisms from an infinite graph @math to a fixed finite constraint graph @math . These spaces become sufficiently tractable when @math is a regular tree (often called a Cayley tree or Bethe lattice) to permit characterization of the constraint graphs @math which admit multiple invariant Gibbs measures. Applications to a physics problem (multiple critical points for symmetry-breaking) and a combinatorics problem (random coloring), as well as some new combinatorial notions, will be presented. Historically, papers have been physically bound to the journal in which they were published; but in the digital age papers are available individually, no longer tied to their respective journals. Hence, papers now can be read and cited based on their own merits, independently of the journal's physical availability, reputation, or impact factor (IF). We compare the strength of the relationship between journals' IFs and the actual citations received by their respective papers from 1902 to 2009. Throughout most of the 20th century, papers' citation rates were increasingly linked to their respective journals' IFs. However, since 1990, the advent of the digital age, the relation between IFs and paper citations has been weakening. This began first in physics, a field that was quick to make the transition into the electronic domain. Furthermore, since 1990 the overall proportion of highly cited papers coming from highly cited journals has been decreasing and, of these highly cited papers, the proportion not coming from highly cited journals has been increasing. Should this pattern continue, it might bring an end to the use of the IF as a way to evaluate the quality of journals, papers, and researchers. © 2012 Wiley Periodicals, Inc. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . Let @math be a nontrivial @math -ary predicate. Consider a random instance of the constraint satisfaction problem @math on @math variables with @math constraints, each being @math applied to @math randomly chosen literals. Provided the constraint density satisfies @math , such an instance is unsatisfiable with high probability. The problem is to efficiently find a proof of unsatisfiability. We show that whenever the predicate @math supports a @math - probability distribution on its satisfying assignments, the sum of squares (SOS) algorithm of degree @math (which runs in time @math ) refute a random instance of @math . In particular, the polynomial-time SOS algorithm requires @math constraints to refute random instances of CSP @math when @math supports a @math -wise uniform distribution on its satisfying assignments. Together with recent work of [LRS15], our result also implies that polynomial-size semidefinite programming relaxation for refutation requires at least @math constraints. Our results (which also extend with no change to CSPs over larger alphabets) subsume all previously known lower bounds for semialgebraic refutation of random CSPs. For every constraint predicate @math , they give a three-way hardness tradeoff between the density of constraints, the SOS degree (hence running time), and the strength of the refutation. By recent algorithmic results of [AOW15] and [RRS16], this full three-way tradeoff is , up to lower-order factors. A new form of document coupling called co-citation is defined as the frequency with which two documents are cited together. The co-citation frequency of two scientific papers can be determined by comparing lists of citing documents in the Science Citation Index and counting identical entries. Networks of co-cited papers can be generated for specific scientific specialties, and an example is drawn from the literature of particle physics. Co-citation patterns are found to differ significantly from bibliographic coupling patterns, but to agree generally with patterns of direct citation. Clusters of co-cited papers provide a new way to study the specialty structure of science. They may provide a new approach to indexing and to the creation of SDI profiles.