The Complexity of Counting Problems Over Incomplete Databases

We study the complexity of various fundamental counting problems that arise in the context of incomplete databases, i.e., relational databases that can contain unknown values in the form of labeled nulls. Specifically, we assume that the domains of these unknown values are finite and, for a Boolean query q , we consider the following two problems: Given as input an incomplete database D , (a) return the number of completions of D that satisfy q ; or (b) return the number of valuations of the nulls of D yielding a completion that satisfies q . We obtain dichotomies between #P-hardness and polynomial-time computability for these problems when q is a self-join–free conjunctive query and study the impact on the complexity of the following two restrictions: (1) every null occurs at most once in D (what is called Codd tables ); and (2) the domain of each null is the same. Roughly speaking, we show that counting completions is much harder than counting valuations: For instance, while the latter is always in #P, we prove that the former is not in #P under some widely believed theoretical complexity assumption. Moreover, we find that both (1) and (2) can reduce the complexity of our problems. We also study the approximability of these problems and show that, while counting valuations always has a fully polynomial-time randomized approximation scheme (FPRAS), in most cases counting completions does not. Finally, we consider more expressive query languages and situate our problems with respect to known complexity classes.

Decision tree classifiers for unmanned aircraft configuration selection

Purpose This paper aims to investigate the possibility of lowering the time taken during the aircraft design for unmanned aerial vehicles by using machine learning (ML) for the configuration selection phase. In this work, a database of unmanned aircraft is compiled and is proposed that decision tree classifiers (DTC) can understand the relations between mission and operational requirements and the resulting aircraft configuration. Design/methodology/approach This paper presents a ML-based approach to configuration selection of unmanned aircraft. Multiple DTC are built to predict the overall configuration. The classifiers are trained with a database of 118 unmanned aircraft with 57 characteristics, 47 of which are inputs for the classification problem, and 10 are the desired outputs, such as wing configuration or engine type. Findings This paper shows that DTC can be used for the configuration selection of unmanned aircraft with reasonable accuracy, understanding the connections between the different mission requirements and the culminating configuration. The framework is also capable of dealing with incomplete databases, maximizing the available knowledge. Originality/value This paper increases the computational usage for the aircraft design while retaining requirements’ traceability and increasing decision awareness.

Unholy goals and flawed methods

A problematic practice has evolved, which is threatening to undermine research in the social sciences and humanities. Bibliometrics is often claimed to be able to measure researchers’ efficiency. We find this quite problematic and, in this article, we illustrate this point by discussing two different bibliometric practices. One is the so-called h-index, the other the so-called BFI-points (Den bibliometriske Forskningsindikator, The Bibliometric Research Indicator). The BFI was never intended to be used for evaluating individual researchers and their productivity. Yet since its introduction in 2008 especially the social sciences and the humanities experience a pressure to deliver “BFI points” and academic job advertisements within the social sciences and the humanities increasingly mention expectations for people’s past and/or future production of BFI points. The h-index is even more problematic because no one academic database covers all the research publications in the world. The whole thing is completely disorganized, and as many as five different h-indexes exist for each researcher. What makes the h-index even more useless is that it will not let you make comparisons across disciplines. Furthermore, like other simple measurements, it is liable to be manipulated and misinterpreted. On that background, it is remarkable that numbers extracted from incomplete databases are used for describing the quality of researchers and their institutions.

Toward an Axiomatization of Strongly Possible Functional Dependencies

In general, there are two main approaches to handle the missing data values problem in SQL tables. One is to ignore or remove any record with some missing data values. The other approach is to fill or impute the missing data with new values [A. Farhangfar, L. A. Kurgan and W. Pedrycz, A novel framework for imputation of missing values in databases, IEEE Trans. Syst. Man Cybern. A, Syst. Hum. 37(5) (2007) 692–709]. In this paper, the second method is considered. Possible worlds, possible and certain keys, and weak and strong functional dependencies were introduced in Refs. 4 and 2 [H. Köhler, U. Leck, S. Link and X. Zhou, Possible and certain keys for SQL, VLDB J. 25(4) (2016) 571–596; M. Levene and G. Loizou, Axiomatisation of functional dependencies in incomplete relations, Theor. Comput. Sci. 206(1) (1998) 283–300]. We introduced the intermediate concept of strongly possible worlds in a preceding paper, which are obtained by filling missing data values with values already existing in the table. Using strongly possible worlds, strongly possible keys and strongly possible functional dependencies (spFDs) were introduced in Refs. 5 and 1 [M. Alattar and A. Sali, Keys in relational databases with nulls and bounded domains, in ADBIS 2019: Advances in Databases and Information Systems, Lecture Notes in Computer Science, Vol. 11695 (Springer, Cham, 2019), pp. 33–50; Functional dependencies in incomplete databases with limited domains, in FoiKS 2020: Foundations of Information and Knowledge Systems, Lecture Notes in Computer Science, Vol. 12012 (Springer, Cham, 2020), pp. 1–21]. In this paper, some axioms and rules for strongly possible functional dependencies are provided, These axioms and rules form the basis for a possible axiomatization of spFDs. For that, we analyze which weak/strong functional dependency and certain functional dependency axioms remain sound for strongly possible functional dependencies, and for the axioms that are not sound, we give appropriate modifications for soundness.

Knowledge-Preserving Certain Answers for SQL-like Queries

Answering queries over incomplete data is based on finding answers that are certainly true, independently of how missing values are interpreted. This informal description has given rise to several different mathematical definitions of certainty. To unify them, a framework based on "explanations", or extra information about incomplete data, was recently proposed. It partly succeeded in justifying query answering methods for relational databases under set semantics, but had two major limitations. First, it was firmly tied to the set data model, and a fixed way of comparing incomplete databases with respect to their information content. These assumptions fail for real-life database queries in languages such as SQL that use bag semantics instead. Second, it was restricted to queries that only manipulate data, while in practice most analytical SQL queries invent new values, typically via arithmetic operations and aggregation. To leverage our understanding of the notion of certainty for queries in SQL-like languages, we consider incomplete databases whose information content may be enriched by additional knowledge. The knowledge order among them is derived from their semantics, rather than being fixed a priori. The resulting framework allows us to capture and justify existing notions of certainty, and extend these concepts to other data models and query languages. As natural applications, we provide for the first time a well-founded definition of certain answers for the relational bag data model and for value-inventing queries on incomplete databases, addressing the key shortcomings of previous approaches.