@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}
}
@article{MichallekGenskeNiehuesetal.2022,
  author    = {Michallek, Florian and Genske, Ulrich and Niehues, Stefan Markus and Hamm, Bernd and Jahnke, Paul},
  title     = {Deep learning reconstruction improves radiomics feature stability and discriminative power in abdominal CT imaging},
  series = {European Radiology},
  volume    = {32},
  journal   = {European Radiology},
  number    = {7},
  publisher = {Springer},
  address   = {New York},
  issn      = {0938-7994},
  doi       = {10.1007/s00330-022-08592-y},
  pages     = {4587 -- 4595},
  year      = {2022},
  abstract  = {Objectives To compare image quality of deep learning reconstruction (AiCE) for radiomics feature extraction with filtered back projection (FBP), hybrid iterative reconstruction (AIDR 3D), and model-based iterative reconstruction (FIRST). Methods Effects of image reconstruction on radiomics features were investigated using a phantom that realistically mimicked a 65-year-old patient's abdomen with hepatic metastases. The phantom was scanned at 18 doses from 0.2 to 4 mGy, with 20 repeated scans per dose. Images were reconstructed with FBP, AIDR 3D, FIRST, and AiCE. Ninety-three radiomics features were extracted from 24 regions of interest, which were evenly distributed across three tissue classes: normal liver, metastatic core, and metastatic rim. Features were analyzed in terms of their consistent characterization of tissues within the same image (intraclass correlation coefficient >= 0.75), discriminative power (Kruskal-Wallis test p value < 0.05), and repeatability (overall concordance correlation coefficient >= 0.75). Results The median fraction of consistent features across all doses was 6\%, 8\%, 6\%, and 22\% with FBP, AIDR 3D, FIRST, and AiCE, respectively. Adequate discriminative power was achieved by 48\%, 82\%, 84\%, and 92\% of features, and 52\%, 20\%, 17\%, and 39\% of features were repeatable, respectively. Only 5\% of features combined consistency, discriminative power, and repeatability with FBP, AIDR 3D, and FIRST versus 13\% with AiCE at doses above 1 mGy and 17\% at doses >= 3 mGy. AiCE was the only reconstruction technique that enabled extraction of higher-order features. Conclusions AiCE more than doubled the yield of radiomics features at doses typically used clinically. Inconsistent tissue characterization within CT images contributes significantly to the poor stability of radiomics features.},
  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}
}