Efficiently querying Description Logic (DL) ontologies is becoming a vital task in various data-intensive DL applications. Considered as a basic service for answering object queries over DL ontologies, instance checking can be realized by using the most specific concept (MSC) method, which converts instance checking into subsumption problems. This method, however, loses its simplicity and efficiency when applied to large and complex ontologies, as it tends to generate very large MSCs that could lead to intractable reasoning. In this paper, we propose a revision to this MSC method for DL SHI , allowing it to generate much simpler and smaller concepts that are specific enough to answer a given query. With independence between computed MSCs, scalability for query answering can also be achieved by distributing and parallelizing the computations. An empirical evaluation shows the efficacy of our revised MSC method and the significant efficiency achieved when using it for answering object queries.
A common direction of these optimization techniques is to reduce the high degree of nondeterminism that is mainly introduced by GCIs in the TBox: given an GCI @math , it can be converted to a disjunction @math , for which a tableau algorithm will have to nondeterministically choose one of the disjuncts for tableau expansion, resulting in an exponential-time behavior of the tableau algorithm w.r.t. the data size. Absorption optimizations @cite_28 @cite_38 @cite_14 were developed to reduce such nondeterminism by combining GCIs for unfoldable concepts, such that the effectiveness of lazy unfolding can be maximized. For example, axioms @math and @math can be combined into @math , where @math is a named concept; then the inference engine can deduce @math if the ABox contains @math . Notice however, this technique may allow only parts of TBox axioms to be absorbed, thus, may not be able to eliminate all sources of nondeterminism especially when ontologies are complex. Based on the absorption optimization, @cite_39 proposed an approach for efficient ABox reasoning for @math that will convert ABox assertions into TBox axioms, apply a absorption technique on the TBox, and covert instance retrieval into concept satisfaction problems.
@cite_28 @cite_38 @cite_14 @cite_39
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We critically evaluate the current state of research in multiple query opGrnization, synthesize the requirements for a modular opCrnizer, and propose an architecture. Our objective is to facilitate future research by providing modular subproblems and a good general-purpose data structure. In rhe context of this archiuzcture. we provide an improved subsumption algorithm. and discuss migration paths from single-query to multiple-query oplimizers. The architecture has three key ingredients. First. each type of work is performed at an appropriate level of abstraction. Segond, a uniform and very compact representation stores all candidate strategies. Finally, search is handled as a discrete optimization problem separable horn the query processing tasks. 1. Problem Definition and Objectives A multiple query optimizer (h4QO) takes several queries as input and seeks to generate a good multi-strategy, an executable operator gaph that simultaneously computes answers to all the queries. The idea is to save by evaluating common subexpressions only once. The commonalities to be exploited include identical selections and joins, predicates that subsume other predicates, and also costly physical operators such as relation scans and SOULS. The multiple query optimization problem is to find a multi-strategy that minimizes the total cost (with overlap exploited). Figure 1 .l shows a multi-strategy generated exploiting commonalities among queries Ql-Q3 at both the logical and physical level. To be really satisfactory, a multi-query optimization algorithm must offer solution quality, ejjiciency, and ease of Permission to copy without fee all a part of this mataial is granted provided that the copies are nut made a diitributed for direct commercial advantage, the VIDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Da Blse Endowment. To copy otherwise. urturepublim identify many kinds of commonalities (e.g., by predicate splitting, sharing relation scans); and search effectively to choose a good combination of l-strategies. Efficiency requires that the optimization avoid a combinatorial explosion of possibilities, and that within those it considers, redundant work on common subexpressions be minimized. ‘Finally, ease of implementation is crucial an algorithm will be practically useful only if it is conceptually simple, easy to attach to an optimizer, and requires relatively little additional soft- Geometric heuristics for the quantifier elimination approach presented by Kapur (2004) are investigated to automatically derive loop invariants expressing weakly relational numerical properties (such as l≤x≤h or l≤±x ±y≤h) for imperative programs. Such properties have been successfully used to analyze commercial software consisting of hundreds of thousands of lines of code (using for example, the Astree tool based on abstract interpretation framework proposed by Cousot and his group). The main attraction of the proposed approach is its much lower complexity in contrast to the abstract interpretation approach (O(n2) in contrast to O(n4), where n is the number of variables) with the ability to still generate invariants of comparable strength. This approach has been generalized to consider disjunctive invariants of the similar form, expressed using maximum function (such as max (x+a,y+b,z+c,d)≤max (x+e,y+f,z+g,h)), thus enabling automatic generation of a subclass of disjunctive invariants for imperative programs as well. This paper considers a sparse signal recovery task in time-varying (time-adaptive) environments. The contribution of the paper to sparsity-aware online learning is threefold; first, a generalized thresholding (GT) operator, which relates to both convex and non-convex penalty functions, is introduced. This operator embodies, in a unified way, the majority of well-known thresholding rules which promote sparsity. Second, a non-convexly constrained, sparsity-promoting, online learning scheme, namely the adaptive projection-based generalized thresholding (APGT), is developed that incorporates the GT operator with a computational complexity that scales linearly to the number of unknowns. Third, the novel family of partially quasi-nonexpansive mappings is introduced as a functional analytic tool for treating the GT operator. By building upon the rich fixed point theory, the previous class of mappings establishes also a link between the GT operator and a union of linear subspaces; a non-convex object which lies at the heart of any sparsity promoting technique, batch or online. Based on this functional analytic framework, a convergence analysis of the APGT is provided. Extensive experiments suggest that the APGT exhibits competitive performance when compared to computationally more demanding alternatives, such as the sparsity-promoting affine projection algorithm (APA)- and recursive least-squares (RLS)-based techniques. We consider the following "efficiently decodable" non-adaptive group testing problem. There is an unknown string x ∈ 0, 1 n with at most d ones in it. We are allowed to test any subset S ⊆ [n] of the indices. The answer to the test tells whether xi = 0 for all i ∈ S or not. The objective is to design as few tests as possible (say, t tests) such that x can be identified as fast as possible (say, poly(t)-time). Efficiently decodable non-adaptive group testing has applications in many areas, including data stream algorithms and data forensics. A non-adaptive group testing strategy can be represented by a t x n matrix, which is the stacking of all the characteristic vectors of the tests. It is well-known that if this matrix is d-disjunct, then any test outcome corresponds uniquely to an unknown input string. Furthermore, we know how to construct d-disjunct matrices with t = O(d2 log n) efficiently. However, these matrices so far only allow for a "decoding" time of O(nt), which can be exponentially larger than poly(t) for relatively small values of d. This paper presents a randomness efficient construction of d-disjunct matrices with t = O(d2 log n) that can be decoded in time poly(d) · t log2 t + O(t2). To the best of our knowledge, this is the first result that achieves an efficient decoding time and matches the best known O(d2 log n) bound on the number of tests. We also derandomize the construction, which results in a polynomial time deterministic construction of such matrices when d = O(log n log log n). A crucial building block in our construction is the notion of (d, l)-list disjunct matrices, which represent the more general "list group testing" problem whose goal is to output less than d + l positions in x, including all the (at most d) positions that have a one in them. List disjunct matrices turn out to be interesting objects in their own right and were also considered independently by [Cheraghchi, FCT 2009]. We present connections between list disjunct matrices, expanders, dispersers and disjunct matrices. List disjunct matrices have applications in constructing (d, l)-sparsity separator structures [Ganguly, ISAAC 2008] and in constructing tolerant testers for Reed-Solomon codes in the data stream model.