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Journal: Theory and Applications of Satisfiability Testing – SAT 2020
Article Title: Taming High Treewidth with Abstraction, Nested Dynamic Programming, and Database Technology
doi: 10.1007/978-3-030-51825-7_25
Figure Lengend Snippet: Graph G (left), a TD \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{T}$$\end{document} of graph G (right).
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Journal: Theory and Applications of Satisfiability Testing – SAT 2020
Article Title: Taming High Treewidth with Abstraction, Nested Dynamic Programming, and Database Technology
doi: 10.1007/978-3-030-51825-7_25
Figure Lengend Snippet: Tables obtained by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsc {\#}\textsc {Sat}_t$$\end{document} on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{T}_{\text {nice}}$$\end{document} for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document} of Example .
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Journal: Theory and Applications of Satisfiability Testing – SAT 2020
Article Title: Taming High Treewidth with Abstraction, Nested Dynamic Programming, and Database Technology
doi: 10.1007/978-3-030-51825-7_25
Figure Lengend Snippet: Selected tables obtained by nested DP on TD \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{T}'$$\end{document} of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_\varphi ^{\{x,y\}}$$\end{document} (left) and on TD \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {T}''$$\end{document} of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_\varphi ^{\{x\}}$$\end{document} (right) for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document} and projection variables \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P=\{x,y\}$$\end{document} of Example via \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathtt {HybDP}_{\textsc {\#}\exists \textsc {Sat}_t}$$\end{document} .
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Journal: Theory and Applications of Satisfiability Testing – SAT 2020
Article Title: Taming High Treewidth with Abstraction, Nested Dynamic Programming, and Database Technology
doi: 10.1007/978-3-030-51825-7_25
Figure Lengend Snippet: Cactus plot of instances for #Sat , where instances (x-axis) are ordered for each solver individually by runtime[seconds] (y-axis). \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {threshold}_{\text {abstr}}=38$$\end{document} .
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Journal: Theory and Applications of Satisfiability Testing – SAT 2020
Article Title: Taming High Treewidth with Abstraction, Nested Dynamic Programming, and Database Technology
doi: 10.1007/978-3-030-51825-7_25
Figure Lengend Snippet: Number of solved \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsc {\#}\exists \textsc {Sat}$$\end{document} insts., grouped by upper bound intervals of treewidth (left), cactus plot (right). time[h] is cumulated wall clock time, timeouts count as 900 s. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {threshold}_{\text {abstr}}\,{=}\,8$$\end{document} .
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Journal: Theory and Applications of Satisfiability Testing – SAT 2020
Article Title: Taming High Treewidth with Abstraction, Nested Dynamic Programming, and Database Technology
doi: 10.1007/978-3-030-51825-7_25
Figure Lengend Snippet: Scatter plot of instances for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsc {\#}\exists \textsc {Sat}$$\end{document} , where the x-axis shows runtime in seconds of nestHDB compared to the y-axis showing runtime of projMC (left) and of ganak (right). \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {threshold}_{\text {abstr}}=8$$\end{document} .
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