Springer Nature - SN SciGraph project Department of Mathematics and Department of Computer Science, Rutgers University, New Brunswick, USA Department of Computer Science, Rutgers University, New Brunswick, USA Department of Mathematics and Department of Computer Science, Rutgers University, New Brunswick, USA Department of Computer Science, Rutgers University, New Brunswick, USA 978-3-662-47671-0 978-3-662-47672-7 Automata, Languages, and Programming Magnús M. Halldórsson Sachdeva Sushant Numerical and Computational Mathematics main results Simultaneous Approximation of Constraint Satisfaction Problems polynomial time 2015-06-20 simultaneous approximation optimization 193-205 direction interesting directions natural meeting point 2015-06-20 time algorithm set collection method chapter true future research nontrivial approximation algorithm first nontrivial approximation algorithm CSP instances CSP problem same set large fraction multiobjective optimization 2022-08-04T17:16 instances max approximation factor improved approximation factor approximation number theory variable v Given k collections of 2SAT clauses on the same set of variables V, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design the first nontrivial approximation algorithms in this context.Our main result is that for every CSP F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {F}}$$\end{document}, for , there is a polynomial time constant factor Pareto approximation algorithm for k simultaneous Max-F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {F}}$$\end{document}-CSP instances. Our methods are quite general, and we also use them to give an improved approximation factor for simultaneous Max-w-SAT (for ). In contrast, for k=ω(logn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k = \omega (\log n)$$\end{document}, no nonzero approximation factor for k simultaneous Max-F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {F}}$$\end{document}-CSP instances can be achieved in polynomial time (assuming the Exponential Time Hypothesis).These problems are a natural meeting point for the theory of constraint satisfaction problems and multiobjective optimization. We also suggest a number of interesting directions for future research. fraction satisfaction problems chapters https://scigraph.springernature.com/explorer/license/ constraint satisfaction problems meeting point point factors https://doi.org/10.1007/978-3-662-47672-7_16 results assignment contrast clauses research context approximation algorithm Bhangale Amey Bettina Speckmann Springer Nature Swastik Kopparty dimensions_id pub.1049324180 Naoki Kobayashi Department of Computer Science, Yale University, New Haven, USA Department of Computer Science, Yale University, New Haven, USA doi 10.1007/978-3-662-47672-7_16 Mathematical Sciences Iwama Kazuo