Advanced tools and methods for treewidth-based problem solving
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Markus Hecher
Dr. Markus Hecher is currently a postdoc at MIT based on two excellence scholarships, where he is supervised by Professor Erik Demaine. He received his PhD from TU Wien (Austria) as well as the University of Potsdam (Germany), according to an individual binational agreement. His research interests revolve around the graph parameter treewidth, focusing on runtime lower bounds and complexity analysis. Markus analyzes problems related to Boolean Satisfiability and richer formalisms such as quantified Boolean Formulas, Answer Set Programming, and further formalisms and problems relevant to AI. For his PhD thesis and his results so far, Markus received several awards like the Austrian Award of Excellence 2021, the EurAI Dissertation Award 2021, and the GI Dissertation Award 2021. For his research so far that combines both theoretical and practical insights, in 2022 he was awarded with the Early Career Award by KR Inc. Markus actively participates in competitions, where he contributed to winning teams several times. For details on his research, achievements, and interests, see
https://dbai.tuwien.ac.at/staff/hecher/ .
Abstract
Computer programs, so-called solvers, for solving the well-known Boolean satisfiability problem (Sat) have been improving for decades. Among the reasons, why these solvers are so fast, is the implicit usage of the formula’s structural properties during solving. One of such structural indicators is the so-called treewidth, which tries to measure how close a formula instance is to being easy (tree-like). This work focuses on logic-based problems and treewidth-based methods and tools for solving them. Many of these problems are also relevant for knowledge representation and reasoning (KR) as well as artificial intelligence (AI) in general. We present a new type of problem reduction, which is referred to by decomposition-guided (DG). This reduction type forms the basis to solve a problem for quantified Boolean formulas (QBFs) of bounded treewidth that has been open since 2004. The solution of this problem then gives rise to a new methodology for proving precise lower bounds for a range of further formalisms in logic, KR, and AI. Despite the established lower bounds, we implement an algorithm for solving extensions of Sat efficiently, by directly using treewidth. Our implementation is based on finding abstractions of instances, which are then incrementally refined in the process. Thereby, our observations confirm that treewidth is an important measure that should be considered in the design of modern solvers.
Funding source: Austrian Science Fund (FWF)
Award Identifier / Grant number: J 4656
Award Identifier / Grant number: P 32830
Funding source: Society for Research Funding in Lower Austria (GFF, Gesellschaft für Forschungsförderung NÖ)
Award Identifier / Grant number: ExzF-0004
Funding source: Vienna Science and Technology Fund (WWTF)
Award Identifier / Grant number: ICT19-065
About the author
Dr. Markus Hecher is currently a postdoc at MIT based on two excellence scholarships, where he is supervised by Professor Erik Demaine. He received his PhD from TU Wien (Austria) as well as the University of Potsdam (Germany), according to an individual binational agreement. His research interests revolve around the graph parameter treewidth, focusing on runtime lower bounds and complexity analysis. Markus analyzes problems related to Boolean Satisfiability and richer formalisms such as quantified Boolean Formulas, Answer Set Programming, and further formalisms and problems relevant to AI. For his PhD thesis and his results so far, Markus received several awards like the Austrian Award of Excellence 2021, the EurAI Dissertation Award 2021, and the GI Dissertation Award 2021. For his research so far that combines both theoretical and practical insights, in 2022 he was awarded with the Early Career Award by KR Inc. Markus actively participates in competitions, where he contributed to winning teams several times. For details on his research, achievements, and interests, see https://dbai.tuwien.ac.at/staff/hecher/.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This research was funded by the Austrian Science Fund (FWF), grants J 4656 and P 32830, the Society for Research Funding in Lower Austria (GFF, Gesellschaft für Forschungsförderung NÖ) grant ExzF-0004, as well as the Vienna Science and Technology Fund (WWTF) grant ICT19-065.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Editorial
- Memristive computing in Germany
- Research Articles
- Bit slicing approaches for variability aware ReRAM CIM macros
- Timing-accurate simulation framework for NVM-based compute-in-memory architecture exploration
- Impact of sneak paths on in-memory logic design in memristive crossbars
- An RRAM-based building block for reprogrammable non-uniform sampling ADCs
- Optimizing multi-level ReRAM memory for low latency and low energy consumption
- Distinguished Dissertations
- Advanced tools and methods for treewidth-based problem solving
Articles in the same Issue
- Frontmatter
- Editorial
- Memristive computing in Germany
- Research Articles
- Bit slicing approaches for variability aware ReRAM CIM macros
- Timing-accurate simulation framework for NVM-based compute-in-memory architecture exploration
- Impact of sneak paths on in-memory logic design in memristive crossbars
- An RRAM-based building block for reprogrammable non-uniform sampling ADCs
- Optimizing multi-level ReRAM memory for low latency and low energy consumption
- Distinguished Dissertations
- Advanced tools and methods for treewidth-based problem solving
