@phdthesis{Hecher2021,
  author    = {Hecher, Markus},
  title     = {Advanced tools and methods for treewidth-based problem solving},
  doi       = {10.25932/publishup-51251},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-512519},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xv, 184},
  year      = {2021},
  abstract  = {In the last decades, there was a notable progress in solving the well-known Boolean satisfiability (Sat) problem, which can be witnessed by powerful Sat solvers. One of the reasons why these solvers are so fast are structural properties of instances that are utilized by the solver's interna. This thesis deals with the well-studied structural property treewidth, which measures the closeness of an instance to being a tree. In fact, there are many problems parameterized by treewidth that are solvable in polynomial time in the instance size when parameterized by treewidth. In this work, we study advanced treewidth-based methods and tools for problems in knowledge representation and reasoning (KR). Thereby, we provide means to establish precise runtime results (upper bounds) for canonical problems relevant to KR. Then, we present a new type of problem reduction, which we call decomposition-guided (DG) that allows us to precisely monitor the treewidth when reducing from one problem to another problem. This new reduction type will be the basis for a long-open lower bound result for quantified Boolean formulas and allows us to design a new methodology for establishing runtime lower bounds for problems parameterized by treewidth. Finally, despite these lower bounds, we provide an efficient implementation of algorithms that adhere to treewidth. Our approach finds suitable abstractions of instances, which are subsequently refined in a recursive fashion, and it uses Sat solvers for solving subproblems. It turns out that our resulting solver is quite competitive for two canonical counting problems related to Sat.},
  language  = {en}
}
@phdthesis{Shaabani2020,
  author    = {Shaabani, Nuhad},
  title     = {On discovering and incrementally updating inclusion dependencies},
  doi       = {10.25932/publishup-47186},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471862},
  school      = {Universit{\"a}t Potsdam},
  pages     = {119},
  year      = {2020},
  abstract  = {In today's world, many applications produce large amounts of data at an enormous rate. Analyzing such datasets for metadata is indispensable for effectively understanding, storing, querying, manipulating, and mining them. Metadata summarizes technical properties of a dataset which rang from basic statistics to complex structures describing data dependencies. One type of dependencies is inclusion dependency (IND), which expresses subset-relationships between attributes of datasets. Therefore, inclusion dependencies are important for many data management applications in terms of data integration, query optimization, schema redesign, or integrity checking. So, the discovery of inclusion dependencies in unknown or legacy datasets is at the core of any data profiling effort. For exhaustively detecting all INDs in large datasets, we developed S-indd++, a new algorithm that eliminates the shortcomings of existing IND-detection algorithms and significantly outperforms them. S-indd++ is based on a novel concept for the attribute clustering for efficiently deriving INDs. Inferring INDs from our attribute clustering eliminates all redundant operations caused by other algorithms. S-indd++ is also based on a novel partitioning strategy that enables discording a large number of candidates in early phases of the discovering process. Moreover, S-indd++ does not require to fit a partition into the main memory--this is a highly appreciable property in the face of ever-growing datasets. S-indd++ reduces up to 50\% of the runtime of the state-of-the-art approach. None of the approach for discovering INDs is appropriate for the application on dynamic datasets; they can not update the INDs after an update of the dataset without reprocessing it entirely. To this end, we developed the first approach for incrementally updating INDs in frequently changing datasets. We achieved that by reducing the problem of incrementally updating INDs to the incrementally updating the attribute clustering from which all INDs are efficiently derivable. We realized the update of the clusters by designing new operations to be applied to the clusters after every data update. The incremental update of INDs reduces the time of the complete rediscovery by up to 99.999\%. All existing algorithms for discovering n-ary INDs are based on the principle of candidate generation--they generate candidates and test their validity in the given data instance. The major disadvantage of this technique is the exponentially growing number of database accesses in terms of SQL queries required for validation. We devised Mind2, the first approach for discovering n-ary INDs without candidate generation. Mind2 is based on a new mathematical framework developed in this thesis for computing the maximum INDs from which all other n-ary INDs are derivable. The experiments showed that Mind2 is significantly more scalable and effective than hypergraph-based algorithms.},
  language  = {en}
}
@phdthesis{Gebser2011,
  author    = {Gebser, Martin},
  title     = {Proof theory and algorithms for answer set programming},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-55425},
  school      = {Universit{\"a}t Potsdam},
  year      = {2011},
  abstract  = {Answer Set Programming (ASP) is an emerging paradigm for declarative programming, in which a computational problem is specified by a logic program such that particular models, called answer sets, match solutions. ASP faces a growing range of applications, demanding for high-performance tools able to solve complex problems. ASP integrates ideas from a variety of neighboring fields. In particular, automated techniques to search for answer sets are inspired by Boolean Satisfiability (SAT) solving approaches. While the latter have firm proof-theoretic foundations, ASP lacks formal frameworks for characterizing and comparing solving methods. Furthermore, sophisticated search patterns of modern SAT solvers, successfully applied in areas like, e.g., model checking and verification, are not yet established in ASP solving. We address these deficiencies by, for one, providing proof-theoretic frameworks that allow for characterizing, comparing, and analyzing approaches to answer set computation. For another, we devise modern ASP solving algorithms that integrate and extend state-of-the-art techniques for Boolean constraint solving. We thus contribute to the understanding of existing ASP solving approaches and their interconnections as well as to their enhancement by incorporating sophisticated search patterns. The central idea of our approach is to identify atomic as well as composite constituents of a propositional logic program with Boolean variables. This enables us to describe fundamental inference steps, and to selectively combine them in proof-theoretic characterizations of various ASP solving methods. In particular, we show that different concepts of case analyses applied by existing ASP solvers implicate mutual exponential separations regarding their best-case complexities. We also develop a generic proof-theoretic framework amenable to language extensions, and we point out that exponential separations can likewise be obtained due to case analyses on them. We further exploit fundamental inference steps to derive Boolean constraints characterizing answer sets. They enable the conception of ASP solving algorithms including search patterns of modern SAT solvers, while also allowing for direct technology transfers between the areas of ASP and SAT solving. Beyond the search for one answer set of a logic program, we address the enumeration of answer sets and their projections to a subvocabulary, respectively. The algorithms we develop enable repetition-free enumeration in polynomial space without being intrusive, i.e., they do not necessitate any modifications of computations before an answer set is found. Our approach to ASP solving is implemented in clasp, a state-of-the-art Boolean constraint solver that has successfully participated in recent solver competitions. Although we do here not address the implementation techniques of clasp or all of its features, we present the principles of its success in the context of ASP solving.},
  language  = {en}
}