On The Power of Tree Projections: Structural Tractability of Enumerating CSP Solutions

The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a computation problem where the focus is either on finding one solution, or on enumerating all solutions, possibly projected to some given set of output variables. The paper investigates the structural tractability of the problem of enumerating (possibly projected) solutions, where tractability means here computable with polynomial delay (WPD), since in general exponentially many solutions may be computed. A general framework based on the notion of tree projection of hypergraphs is considered, which generalizes all known decomposition methods. Tractability results have been obtained both for classes of structures where output variables are part of their specification, and for classes of structures where computability WPD must be ensured for any possible set of output variables. These results are shown to be tight, by exhibiting dichotomies for classes of structures having bounded arity and where the tree decomposition method is considered

Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic

The hypergraph duality problem DUAL is defined as follows: given two simple hypergraphs $\mathcal{G}$ and $\mathcal{H}$, decide whether $\mathcal{H}$ consists precisely of all minimal transversals of $\mathcal{G}$ (in which case we say that $\mathcal{G}$ is the dual of $\mathcal{H}$). This problem is equivalent to deciding whether two given non-redundant monotone DNFs are dual. It is known that non-DUAL, the complementary problem to DUAL, is in $\mathrm{GC}(\log^2 n,\mathrm{PTIME})$, where $\mathrm{GC}(f(n),\mathcal{C})$ denotes the complexity class of all problems that after a nondeterministic guess of $O(f(n))$ bits can be decided (checked) within complexity class $\mathcal{C}$. It was conjectured that non-DUAL is in $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. In this paper we prove this conjecture and actually place the non-DUAL problem into the complexity class $\mathrm{GC}(\log^2 n,\mathrm{TC}^0)$ which is a subclass of $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. We here refer to the logtime-uniform version of $\mathrm{TC}^0$, which corresponds to $\mathrm{FO(COUNT)}$, i.e., first order logic augmented by counting quantifiers. We achieve the latter bound in two steps. First, based on existing problem decomposition methods, we develop a new nondeterministic algorithm for non-DUAL that requires to guess $O(\log^2 n)$ bits. We then proceed by a logical analysis of this algorithm, allowing us to formulate its deterministic part in $\mathrm{FO(COUNT)}$. From this result, by the well known inclusion $\mathrm{TC}^0\subseteq\mathrm{LOGSPACE}$, it follows that DUAL belongs also to $\mathrm{DSPACE}[\log^2 n]$. Finally, by exploiting the principles on which the proposed nondeterministic algorithm is based, we devise a deterministic algorithm that, given two hypergraphs $\mathcal{G}$ and $\mathcal{H}$, computes in quadratic logspace a transversal of $\mathcal{G}$ missing in $\mathcal{H}$.Comment: Restructured the presentation in order to be the extended version of a paper that will shortly appear in SIAM Journal on Computin

Computing FO-Rewritings in EL in Practice: from Atomic to Conjunctive Queries

A prominent approach to implementing ontology-mediated queries (OMQs) is to rewrite into a first-order query, which is then executed using a conventional SQL database system. We consider the case where the ontology is formulated in the description logic EL and the actual query is a conjunctive query and show that rewritings of such OMQs can be efficiently computed in practice, in a sound and complete way. Our approach combines a reduction with a decomposed backwards chaining algorithm for OMQs that are based on the simpler atomic queries, also illuminating the relationship between first-order rewritings of OMQs based on conjunctive and on atomic queries. Experiments with real-world ontologies show promising results

Towards Efficient Reasoning under Guarded-based Disjunctive Existential Rules

International audienceThe complete picture of the complexity of answering (unions of) conjunctive queries under the main guarded-based classes of disjunc- tive existential rules has been recently settled. It has been shown that the problem is very hard, namely 2ExpTime-complete, even for fixed sets of rules expressed in lightweight formalisms. This gives rise to the question whether its complexity can be reduced by restricting the query language. Several subclasses of conjunctive queries have been proposed with the aim of reducing the complexity of classical database problems such as query evaluation and query containment. Three of the most prominent subclasses of this kind are queries of bounded hypertree-width, queries of bounded treewidth and acyclic queries. The central objective of the present paper is to understand whether the above query languages have a positive impact on the complexity of query answering under the main guarded-based classes of disjunctive existential rules. We show that (unions of) conjunctive queries of bounded hypertree- width and of bounded treewidth do not reduce the complexity of our problem, even if we focus on predicates of bounded arity, or on fixed sets of disjunctive existential rules. Regarding acyclic queries, although our problem remains 2ExpTime-complete in general, in some relevant set- tings the complexity reduces to ExpTime-complete; in fact, this requires to bound the arity of the predicates, and for some expressive guarded- based formalisms, to fix the set of rules

Ontology-Based Data Access and Integration

An ontology-based data integration (OBDI) system is an information management system consisting of three components: an ontology, a set of data sources, and the mapping between the two. The ontology is a conceptual, formal description of the domain of interest to a given organization (or a community of users), expressed in terms of relevant concepts, attributes of concepts, relationships between concepts, and logical assertions characterizing the domain knowledge. The data sources are the repositories accessible by the organization where data concerning the domain are stored. In the general case, such repositories are numerous, heterogeneous, each one managed and maintained independently from the others. The mapping is a precise specification of the correspondence between the data contained in the data sources and the elements of the ontology. The main purpose of an OBDI system is to allow information consumers to query the data using the elements in the ontology as predicates. In the special case where the organization manages a single data source, the term ontology-based data access (ODBA) system is used

Application strategy for an anthraquinonebased repellent and the protection of soybeans from Canada goose depredation

Agricultural crops can sustain extensive damage caused by Canada geese (Branta canadensis) when these crops are planted near wetlands or brood-rearing sites. From 2000 to 2015, South Dakota Game, Fish and Parks spent \u3e$5.6 million to manage damages caused by Canada geese to agricultural crops (primarily soybeans) in South Dakota, USA. For the purpose of developing a repellent application strategy for nonlethal goose damage management, we comparatively evaluated the width of anthraquinone applications (i.e., 9.4 L Flight Control® Plus goose repellent/ha [active ingredient: 50% 9,10-anthraquinone] at 0–36 m versus 0–73 m perpendicular to the edge of wetlands in 2014), the timing of the first repellent application (i.e., 9.4 L Flight Control Plus goose repellent/ha at 50% versus 75% seedling emergence in 2015), the yield of soybeans (Glycine max) within repellent-treated and untreated subplots, and anthraquinone chemical residues in Day County, South Dakota. Soybean yield was greater in subplots 73 m from the water’s edge than that in the 36-m subplots (P \u3c 0.02). Among subplots first sprayed at 50% seedling emergence, soybean yield was greater at 73 m and 82 m than that at 36 m (P \u3c 0.005). In contrast, we observed no difference in yield at 36 m, 73 m, or 82 m in the subplots first sprayed at 72% seedling emergence (P \u3e 0.09). We therefore conclude that goose damages were effectively managed in subplots first sprayed at 72% seedling emergence. Anthraquinone residues averaged 674 and 629 ppm anthraquinone upon the first application of the repellent (June to July), 22 and 35 ppm anthraquinone in the mid-season hay (August to September), and 36 and 28 ppb anthraquinone in the harvested seed (October to November) in 2014 and 2015, respectively. Our results suggest that a 73-m bandwidth of anthraquinone-based repellents first applied at approximately 72% or 65–85% seedling emergence can protect soybeans from Canada goose depredation

Application Strategy for an Anthraquinone-Based Repellent and the Protection of Soybeans from Canada Goose Depredation

Agricultural crops can sustain extensive damage caused by Canada geese (Branta canadensis) when these crops are planted near wetlands or brood-rearing sites. From 2000 to 2015, South Dakota Game, Fish and Parks spent \u3e$5.6 million to manage damages caused by Canada geese to agricultural crops (primarily soybeans) in South Dakota, USA. For the purpose of developing a repellent application strategy for nonlethal goose damage management, we comparatively evaluated the width of anthraquinone applications (i.e., 9.4 L Flight Control® Plus goose repellent/ha [active ingredient: 50% 9,10-anthraquinone] at 0–36 m versus 0–73 m perpendicular to the edge of wetlands in 2014), the timing of the first repellent application (i.e., 9.4 L Flight Control Plus goose repellent/ha at 50% versus 75% seedling emergence in 2015), the yield of soybeans (Glycine max) within repellent-treated and untreated subplots, and anthraquinone chemical residues in Day County, South Dakota. Soybean yield was greater in subplots 73 m from the water’s edge than that in the 36-m subplots (P \u3c 0.02). Among subplots first sprayed at 50% seedling emergence, soybean yield was greater at 73 m and 82 m than that at 36 m (P \u3c 0.005). In contrast, we observed no difference in yield at 36 m, 73 m, or 82 m in the subplots first sprayed at 72% seedling emergence (P \u3e 0.09). We therefore conclude that goose damages were effectively managed in subplots first sprayed at 72% seedling emergence. Anthraquinone residues averaged 674 and 629 ppm anthraquinone upon the first application of the repellent (June to July), 22 and 35 ppm anthraquinone in the mid-season hay (August to September), and 36 and 28 ppb anthraquinone in the harvested seed (October to November) in 2014 and 2015, respectively. Our results suggest that a 73-m bandwidth of anthraquinone-based repellents first applied at approximately 72% or 65–85% seedling emergence can protect soybeans from Canada goose depredation

Undirected Graphs of Entanglement Two

Entanglement is a complexity measure of directed graphs that origins in fixed point theory. This measure has shown its use in designing efficient algorithms to verify logical properties of transition systems. We are interested in the problem of deciding whether a graph has entanglement at most k. As this measure is defined by means of games, game theoretic ideas naturally lead to design polynomial algorithms that, for fixed k, decide the problem. Known characterizations of directed graphs of entanglement at most 1 lead, for k = 1, to design even faster algorithms. In this paper we present an explicit characterization of undirected graphs of entanglement at most 2. With such a characterization at hand, we devise a linear time algorithm to decide whether an undirected graph has this property

Redundancy, Deduction Schemes, and Minimum-Size Bases for Association Rules

Association rules are among the most widely employed data analysis methods in the field of Data Mining. An association rule is a form of partial implication between two sets of binary variables. In the most common approach, association rules are parameterized by a lower bound on their confidence, which is the empirical conditional probability of their consequent given the antecedent, and/or by some other parameter bounds such as "support" or deviation from independence. We study here notions of redundancy among association rules from a fundamental perspective. We see each transaction in a dataset as an interpretation (or model) in the propositional logic sense, and consider existing notions of redundancy, that is, of logical entailment, among association rules, of the form "any dataset in which this first rule holds must obey also that second rule, therefore the second is redundant". We discuss several existing alternative definitions of redundancy between association rules and provide new characterizations and relationships among them. We show that the main alternatives we discuss correspond actually to just two variants, which differ in the treatment of full-confidence implications. For each of these two notions of redundancy, we provide a sound and complete deduction calculus, and we show how to construct complete bases (that is, axiomatizations) of absolutely minimum size in terms of the number of rules. We explore finally an approach to redundancy with respect to several association rules, and fully characterize its simplest case of two partial premises.Comment: LMCS accepted pape