Parameterized Complexity and Kernel Bounds for Hard Planning Problems

  • Christer Bäckström
  • Peter Jonsson
  • Sebastian Ordyniak
  • Stefan Szeider
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7878)


The propositional planning problem is a notoriously difficult computational problem. Downey et al. (1999) initiated the parameterized analysis of planning (with plan length as the parameter) and Bäckström et al. (2012) picked up this line of research and provided an extensive parameterized analysis under various restrictions, leaving open only one stubborn case. We continue this work and provide a full classification. In particular, we show that the case when actions have no preconditions and at most e postconditions is fixed-parameter tractable if e ≤ 2 and W[1]-complete otherwise. We show fixed-parameter tractability by a reduction to a variant of the Steiner Tree problem; this problem has been shown fixed-parameter tractable by Guo et al. (2007). If a problem is fixed-parameter tractable, then it admits a polynomial-time self-reduction to instances whose input size is bounded by a function of the parameter, called the kernel. For some problems, this function is even polynomial which has desirable computational implications. Recent research in parameterized complexity has focused on classifying fixed-parameter tractable problems on whether they admit polynomial kernels or not. We revisit all the previously obtained restrictions of planning that are fixed-parameter tractable and show that none of them admits a polynomial kernel unless the polynomial hierarchy collapses to its third level.


Goal State Parameterized Complexity Parameterized Problem Polynomial Kernel Kernel Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Christer Bäckström
    • 1
  • Peter Jonsson
    • 1
  • Sebastian Ordyniak
    • 2
  • Stefan Szeider
    • 3
  1. 1.Department of Computer ScienceLinköping UniversityLinköpingSweden
  2. 2.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic
  3. 3.Institute of Information SystemsVienna University of TechnologyViennaAustria

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