DSpace-CRIS at TU Wienhttps://repositum.tuwien.atThe reposiTUm digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 01 Aug 2021 01:34:49 GMT2021-08-01T01:34:49Z5021Normal forms for non-relational datahttp://hdl.handle.net/20.500.12708/6928Title: Normal forms for non-relational data
Authors: Fischl, Wolfgang
Abstract: The amount of data stored in today`s information systems is increasing rapidly. Most widely used for this task are relational database management systems. However, alternative data formats, like XML documents or graph databases, continue to become more and more popular. In all these data formats database design is an important task to avoid redundancies arising from badly designed schemata. Therefore, Normal Forms were developed. Most prominently, Boyce- Codd Normal Form (BCNF) is used for relational models. Arenas and Libkin introduced 2004 XML Normal Form for XML documents. So far, a normal form for graph databases has not been considered yet. Our goal is to define a normal form that captures the intuition of BCNF for graph databases. We will recall Boyce-Codd Normal Form and XML Normal Form and will then use ideas from these to define a normal form for graph databases. Description Logics (DLs) are ideally suited as a formal model for graph databases. Since BCNF is formulated over functional dependencies (FDs), we need to express FDs over DL knowledge bases (KBs). A first candidate are path-based identification constraints introduced by Calvanese in 2008. However, we show that path-based identification constraints are not powerful enough to model functional dependencies. Therefore, we propose tree-based identification constraints as an extension of path-based identification constraints. Based on tree-based identification constraints we look at redundancy in DLs. The main result of this thesis is a definition of Description Logic Normal Form, which is a faithful translation of BCNF to Description Logics. Additionally, we introduce a direct mapping from relational schemas to DL KBs and show that if a relational schema is in BCNF, then the DL KB, directly mapped from this schema, is in DLNF and vice versa.
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Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/20.500.12708/69282013-01-01T00:00:00ZGeneralized and fractional hypertree decompositions : from theory to practicehttp://hdl.handle.net/20.500.12708/1967Title: Generalized and fractional hypertree decompositions : from theory to practice
Authors: Fischl, Wolfgang
Abstract: Hypertree decompositions, as well as the more powerful generalized hypertree decompositions (GHDs), and the yet more general fractional hypertree decompositions (FHD) are hypergraph decomposition methods successfully used for answering conjunctive queries and for solving constraint satisfaction problems. Every hypergraph H has a width relative to each of these decomposition methods: its hypertree width hw(H), its generalized hypertree width ghw(H), and its fractional hypertree width fhw(H), respectively. It is known that hw(H) k can be checked in polynomial time for fixed k, while checking ghw(H) k is NP-complete for k 3. The complexity of checking fhw(H) k for a fixed k has been open for over a decade. We settle this open problem by showing that checking fhw(H) k is NP-complete, even for k = 2. The same construction allows us to prove also the NP-completeness of checking ghw(H) k for k = 2. After proving these hardness results, we investigate meaningful restrictions, for which checking for bounded ghw and fhw is easy. In particular, we study classes of hypergraphs that enjoy the bounded edge-intersection property (BIP), the more general bounded multi-edge intersection property (BMIP), the bounded degree property (BDP) and the bounded VC-dimension. Given the increasing interest in using such decomposition methods in practice, a publicly accessible repository of decomposition software, as well as a large set of benchmarks, and a web-accessible workbench for inserting, analysing, and retrieving hypergraphs are called for. We address this need by providing (i) concrete implementations of hypergraph decompositions (including new practical algorithms), (ii) a new, comprehensive benchmark of hypergraphs stemming from disparate CQ and CSP collections, and (iii) HyperBench, our new web-interface for accessing the benchmark and the results of our analyses. In addition, we describe a number of actual experiments we carried out with this new infrastructure.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/20.500.12708/19672018-01-01T00:00:00Z