Explaining Activities as Consistent Groups of Events

The Hierarchical Conditional Random Field (HCRF) model have been successfully applied to a number of image labeling problems, including image segmentation. However, existing HCRF models of image segmentation do not allow multiple classes to be assigned to a single region, which limits their ability to incorporate contextual information across multiple scales. At higher scales in the image, this representation yields an oversimplified model since multiple classes can be reasonably expected to appear within large regions. This simplified model particularly limits the impact of information at higher scales. Since class-label information at these scales is usually more reliable than at lower, noisier scales, neglecting this information is undesirable. To address these issues, we propose a new consistency potential for image labeling problems, which we call the harmony potential. It can encode any possible combination of labels, penalizing only unlikely combinations of classes. We also propose an effective sampling strategy over this expanded label set that renders tractable the underlying optimization problem. Our approach obtains state-of-the-art results on two challenging, standard benchmark datasets for semantic image segmentation: PASCAL VOC 2010, and MSRC-21.     

一种量词约束满足问题的混合易解子类

量词约束满足问题是人工智能和自动推理领域的一个重要问题.寻找多项式时间易解子类,是研究此类问题计算复杂性的关键.通过分析二元量词约束满足问题中的约束关系特征,以及量词前缀中的全称量词排列的顺序,提出了针对全称量词变量子结构的易解性质的分析方法.通过该方法,扩展了已知的基于Broken-Triangle Property的多项式时间易解子类,提出了一个更一般化的量词约束满足问题的混合易解子类.讨论了易解子类在问题结构分析中的一个应用,即通过易解子类确定量词约束满足问题的隐蔽变量集合,并通过实验分析不同易解子类所确定的集合大小.实验改造了基于回溯算法的求解器,在回溯过程中加入了易解子类的识别算法,并采用随机约束满足问题的生成模型作为测试基准.通过对比实验,验证了提出的多项式时间易解子类可以识别出更小的隐蔽变量集合,因此,新提出的易解子类在确定隐蔽变量集合方面更具优势.最后阐述了其他已有的混合易解子类也可以通过类似方法进行扩展,从而得到更多的一般化的理论结果.     

Tractability in constraint satisfaction problems: a survey

Even though the Constraint Satisfaction Problem (CSP) is NP-complete, many tractable classes of CSP instances have been identified. After discussing different forms and uses of tractability, we describe some landmark tractable classes and survey recent theoretical results. Although we concentrate on the classical CSP, we also cover its important extensions to infinite domains and optimisation, as well as #CSP and QCSP.     

A polynomial relational class of binary CSP

Finding a solution to a constraint satisfaction problem (CSP) is known to be an NP-hard task. Considerable effort has been spent on identifying tractable classes of CSP, in other words, classes of constraint satisfaction problems for which there are polynomial time recognition and resolution algorithms. In this article, we present a relational tractable class of binary CSP. Our key contribution is a new ternary operation that we name mjx. We first characterize mjx-closed relations which leads to an optimal algorithm to recognize such relations. To reduce space and time complexity, we define a new storage technique for these relations which reduces the complexity of establishing a form of strong directional path consistency, the consistency level that solves all instances of the proposed class (and, indeed, of all relational classes closed under a majority polymorphism).     

Implementing a Test for Tractability

The question of determining which sets of constraints give rise to NP-complete problems, and which give rise to tractable problems, is an important open problem in the theory of constraint satisfaction. It has been shown in previous papers that certain sufficient conditions for tractability and NP-completeness can be identified using algebraic properties of relations, and that these conditions can be tested by solving a particular form of constraint satisfaction problem (the so-called indicator problem).This paper describes a program which can solve the relevant indicator problems for arbitrary sets of constraints over small domains, and for some sets of constraints over larger domains. The main innovation in the program is its ability to deal with the many symmetries present in the problem; it also has the ability to preserve symmetries in cases where this speeds up the solution.Using this program, we have systematically investigated the complexity of all individual binary relations over a domain of size four or less, and of all individual ternary relations over a domain of size three or less. This automated analysis includes the derivation of more than 450 000 new NP-completeness results, and precisely identifies the small set of individual relations which cannot be classified as either tractable or NP-complete using the algebraic conditions presented in previous papers.     

Disjunctions, independence, refinements

An important question in constraint satisfaction is how to restrict the problem to ensure tractability (since the general problem is NP-hard). The use of disjunctions has proven to be a useful method for constructing tractable constraint classes from existing classes; the well-known ‘max-closed’ and ‘ORD-Horn’ constraints are examples of tractable classes that can be constructed this way. Three sufficient conditions (the guaranteed satisfaction property, 1-independence and 2-independence) that each ensure the tractability of constraints combined by disjunctions have been proposed in the literature. We show that these conditions are both necessary and sufficient for tractability in three different natural classes of disjunctive constraints. This suggests that deciding this kind of property is a very important task when dealing with disjunctive constraints. We provide a simple, automatic method for checking the 1-independence property—this method is applicable whenever the consistency of the constraints under consideration can be decided by path-consistency. Our method builds on a connection between independence and refinements (which is a way of reducing one constraint satisfaction problem to another.)     

Structural decompositions for problems with global constraints

A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed combinations of values, or implicitly, by special-purpose algorithms provided by a solver. Such implicitly represented constraints, known as global constraints, are widely used; indeed, they are one of the key reasons for the success of constraint programming in solving real-world problems. In recent years, a variety of restrictions on the structure of CSP instances have been shown to yield tractable classes of CSPs. However, most such restrictions fail to guarantee tractability for CSPs with global constraints. We therefore study the applicability of structural restrictions to instances with such constraints. We show that when the number of solutions to a CSP instance is bounded in key parts of the problem, structural restrictions can be used to derive new tractable classes. Furthermore, we show that this result extends to combinations of instances drawn from known tractable classes, as well as to CSP instances where constraints assign costs to satisfying assignments.     

New tractable classes for default reasoning from conditional knowledge bases

This paper refines the tractability/intractability frontier of default reasoning from conditional knowledge bases. It presents two new tractable cases with relation to lexicographic entailment. In particular, we have introduced nested conditional knowledge bases and co-nested conditional knowledge bases, which are meaningful conditional knowledge bases. Both tractable classes presented in this paper can be recognized in linear time.     

COMPLEXITY RESULTS FOR SAS+ PLANNING

We have previously reported a number of tractable planning problems defined in the SAS⁺ formalism. This article complements these results by providing a complete map over the complexity of SAS⁺ planning under all combinations of the previously considered restrictions. We analyze the complexity of both finding a minimal plan and finding any plan. In contrast to other complexity surveys of planning, we study not only the complexity of the decision problems but also the complexity of the generation problems. We prove that the SAS⁺-PUS problem is the maximal tractable problem under the restrictions we have considered if we want to generate minimal plans. If we are satisfied with any plan, then we can generalize further to the SAS⁺-US problem, which we prove to be the maximal tractable problem in this case.     

Backdoor Sets of Quantified Boolean Formulas

We generalize the notion of backdoor sets from propositional formulas to quantified Boolean formulas (QBF). This allows us to obtain hierarchies of tractable classes of quantified Boolean formulas with the classes of quantified Horn and quantified 2CNF formulas, respectively, at their first level, thus gradually generalizing these two important tractable classes. In contrast to known tractable classes based on bounded treewidth, the number of quantifier alternations of our classes is unbounded. As a side product of our considerations we develop a theory of variable dependency which is of independent interest.     

Tractable classes for CSPs of arbitrary arity: from theory to practice

The research of this thesis focuses on the analysis of polynomial classes and their practical exploitation for solving constraint satisfaction problems (CSPs) with finite domains. In particular, I worked on bridging the gap between theoretical works and practical results in constraint solvers. Specifically, the goal of this thesis is to find explanation for the effectiveness of solvers, and also to show that studied tractable classes are not artificial since several real-problems among the ones used in the CSP 2008 Competition belong to them.Our work is organized into three main parts. In the first part, we proposed several types of microstructures for CSPs of arbitrary arity which are based on some knwon binary encoding of non-binary CSPs like, dual encoding, hidden-variable transformation and mixed (or double) encoding. These theoretical tools are designed to facilitate the study of tractable classes, sets of CSP instances which can be solved in polytime, when the constraints are non-binary. After that, we propose a new tractable classes of CSPs whose the highlighting should allow on the one hand to explain the effectiveness of solvers of the state of the art namely FC, MAC, RFL and on the second hand to provide the opportunities for easy integration in these solvers. These would include the definition of new tractable classes without using of an ad hoc algorithms as in the traditional case. These new tractable classes are related to the number of maximal cliques in the microstructure of binary or non-binary CSP. In the last part, we focus on the presence of instances belonging to polynomial classes in classical benchmarks used by the CP community. We study in particular the Broken-Triangle Property (BTP) and its extension DBTP to CSP of arbitrary arity. Next, we prove that BTP can also be used to reduce the size of the search space by merging pairs of values on which no broken triangle exists. Finally, we introduce a formal framework, called transformation, and we develop the concept of hidden tractable class that we exploit from an experimental point of view.     

Version spaces and the consistency problem

A version space is a collection of concepts consistent with a given set of positive and negative examples. Mitchell [Artificial Intelligence 18 (1982) 203-226] proposed representing a version space by its boundary sets: the maximally general (G) and maximally specific consistent concepts (S). For many simple concept classes, the size of G and S is known to grow exponentially in the number of positive and negative examples. This paper argues that previous work on alternative representations of version spaces has disguised the real question underlying version space reasoning. We instead show that tractable reasoning with version spaces turns out to depend on the consistency problem, i.e., determining if there is any concept consistent with a set of positive and negative examples. Indeed, we show that tractable version space reasoning is possible if and only if there is an efficient algorithm for the consistency problem. Our observations give rise to new concept classes for which tractable version space reasoning is now possible, e.g., 1-decision lists, monotone depth two formulas, and halfspaces.     

Inference Methods for CRFs with Co-occurrence Statistics

The Markov and Conditional random fields (CRFs) used in computer vision typically model only local interactions between variables, as this is generally thought to be the only case that is computationally tractable. In this paper we consider a class of global potentials defined over all variables in the CRF. We show how they can be readily optimised using standard graph cut algorithms at little extra expense compared to a standard pairwise field. This result can be directly used for the problem of class based image segmentation which has seen increasing recent interest within computer vision. Here the aim is to assign a label to each pixel of a given image from a set of possible object classes. Typically these methods use random fields to model local interactions between pixels or super-pixels. One of the cues that helps recognition is global object co-occurrence statistics, a measure of which classes (such as chair or motorbike) are likely to occur in the same image together. There have been several approaches proposed to exploit this property, but all of them suffer from different limitations and typically carry a high computational cost, preventing their application on large images. We find that the new model we propose produces a significant improvement in the labelling compared to just using a pairwise model and that this improvement increases as the number of labels increases.     

Mining frequent conjunctive queries using functional and inclusion dependencies

We address the issue of mining frequent conjunctive queries in a relational database, a problem known to be intractable even for conjunctive queries over a single table. In this article, we show that mining frequent projection-selection-join queries becomes tractable if joins are performed along keys and foreign keys, in a database satisfying functional and inclusion dependencies, under certain restrictions. We note that these restrictions cover most practical cases, including databases operating over star schemas, snow-flake schemas and constellation schemas. In our approach, we define an equivalence relation over queries using a pre-ordering with respect to which the support is shown to be anti-monotonic. We propose a level-wise algorithm for computing all frequent queries by exploiting the fact that equivalent queries have the same support. We report on experiments showing that, in our context, mining frequent projection-selection-join queries is indeed tractable, even for large data sets.     

Assigning multiple job types to parallel specialized servers

In this paper methods of mixing decision rules are investigated and applied to the so-called multiple job type assignment problem with specialized servers. This problem is modeled as continuous time Markov decision process. For this assignment problem performance optimization is in general considered to be difficult. Moreover, for optimal dynamic Markov decision policies the corresponding decision rules have in general a complicated structure not facilitating a smooth implementation. On the other hand optimization over the subclass of so-called static policies is known to be tractable. In the current paper a suitable static decision rule is mixed with dynamic decision rules which are selected such that these rules are relatively easy to describe and implement. Some mixing methods are discussed and optimization is performed over corresponding classes of so-called mixing policies. These mixing policies maintain the property that they are easy to describe and implement compared to overall optimal dynamic Markov decision policies. Besides for all investigated instances the optimized mixing policies perform substantially better than optimal static policies.     

The power of propagation: when GAC is enough

Considerable effort in constraint programming has focused on the development of efficient propagators for individual constraints. In this paper, we consider the combined power of such propagators when applied to collections of more than one constraint. In particular we identify classes of constraint problems where such propagators can decide the existence of a solution on their own, without the need for any additional search. Sporadic examples of such classes have previously been identified, including classes based on restricting the structure of the problem, restricting the constraint types, and some hybrid examples. However, there has previously been no unifying approach which characterises all of these classes: structural, language-based and hybrid. In this paper we develop such a unifying approach and embed all the known classes into a common framework. We then use this framework to identify a further class of problems that can be solved by propagation alone.     

Complexity of Clausal Constraints Over Chains

We investigate the complexity of the satisfiability problem of constraints over finite totally ordered domains. In our context, a clausal constraint is a disjunction of inequalities of the form x≥d and x≤d. We classify the complexity of constraints based on clausal patterns. A pattern abstracts away from variables and contains only information about the domain elements and the type of inequalities occurring in a constraint. Every finite set of patterns gives rise to a (clausal) constraint satisfaction problem in which all constraints in instances must have an allowed pattern. We prove that every such problem is either polynomially decidable or NP-complete, and give a polynomial-time algorithm for recognizing the tractable cases. Some of these tractable cases are new and have not been previously identified in the literature.     

Toward incremental computation of argumentation semantics: A decomposition-based approach

Currently, except some classes of argumentation frameworks (with special topologies or fixed parameters, such as acyclic, symmetric, and bounded tree-width, etc.) that have been clearly identified as tractable, for a generic argumentation framework (also called a defeat graph), how to efficiently compute its semantics is still a challenging problem. Inspired by the local tractability of an argumentation framework, we first propose a decomposition-based approach, and then conduct an empirical investigation. Given a generic argumentation framework, it is firstly decomposed into a set of sub-frameworks that are located in a number of layers. Then, the semantics of an argumentation framework are computed incrementally, from the lowest layer in which each sub-framework is not restricted by other sub-frameworks, to the highest layer in which each sub-framework is most restricted by the sub-frameworks located in the lower layers. In each iteration, the semantics of each sub-framework is computed locally, while the combination of semantics of a set of sub-frameworks is performed in two dimensions: horizontally and vertically. The average results show that when the ratio of the number of edges to the number of nodes of a defeat graph is less than 1.5:1, the decomposition-based approach is obviously efficient.     

Algorithms and complexity results for persuasive argumentation

The study of arguments as abstract entities and their interaction as introduced by Dung (1995) [1] has become one of the most active research branches within Artificial Intelligence and Reasoning. A main issue for abstract argumentation systems is the selection of acceptable sets of arguments. Value-based argumentation, as introduced by Bench-Capon (2003) [8], extends Dung?s framework. It takes into account the relative strength of arguments with respect to some ranking representing an audience: an argument is subjectively accepted if it is accepted with respect to some audience, it is objectively accepted if it is accepted with respect to all audiences.Deciding whether an argument is subjectively or objectively accepted, respectively, are computationally intractable problems. In fact, the problems remain intractable under structural restrictions that render the main computational problems for non-value-based argumentation systems tractable. In this paper we identify nontrivial classes of value-based argumentation systems for which the acceptance problems are polynomial-time tractable. The classes are defined by means of structural restrictions in terms of the underlying graphical structure of the value-based system. Furthermore we show that the acceptance problems are intractable for two classes of value-based systems that where conjectured to be tractable by Dunne (2007) [12].