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Backdoors to Satisfaction

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The Multivariate Algorithmic Revolution and Beyond

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7370))

Abstract

A backdoor set is a set of variables of a propositional formula such that fixing the truth values of the variables in the backdoor set moves the formula into some polynomial-time decidable class. If we know a small backdoor set we can reduce the question of whether the given formula is satisfiable to the same question for one or several easy formulas that belong to the tractable class under consideration. In this survey we review parameterized complexity results for problems that arise in the context of backdoor sets, such as the problem of finding a backdoor set of size at most k, parameterized by k. We also discuss recent results on backdoor sets for problems that are beyond NP.

Research supported by the European Research Council (ERC), project COMPLEX REASON 239962.

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  1. Institute of Information Systems, Vienna University of Technology, A-1040, Vienna, Austria

    Serge Gaspers & Stefan Szeider

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  1. Serge Gaspers
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  2. Stefan Szeider
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  1. Department of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands

    Hans L. Bodlaender

  2. School of Mathematics, Statistics and Operations Research, Victoria University, P.O. Box 600, Wellington, New Zealand

    Rod Downey

  3. Institute of Informatics, University of Bergen, Postboks 7800, 5020, Bergen, Norway

    Fedor V. Fomin

  4. Computer and Automation Research Institute, Hungarian Academy of Sciences (MTA SZTAKI), Pf. 63, 1518, Budapest, Hungary

    Dániel Marx

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Gaspers, S., Szeider, S. (2012). Backdoors to Satisfaction. In: Bodlaender, H.L., Downey, R., Fomin, F.V., Marx, D. (eds) The Multivariate Algorithmic Revolution and Beyond. Lecture Notes in Computer Science, vol 7370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30891-8_15

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