The Complexity of Planning Revisited - A Parameterized Analysis

The early classifications of the computational complexity of planning under various restrictions in STRIPS (Bylander) and SAS+ (Backstrom and Nebel) have influenced following research in planning in many ways. We go back and reanalyse their subclasses, but this time using the more modern tool of parameterized complexity analysis. This provides new results that together with the old results give a more detailed picture of the complexity landscape. We demonstrate separation results not possible with standard complexity theory, which contributes to explaining why certain cases of planning have seemed simpler in practice than theory has predicted. In particular, we show that certain restrictions of practical interest are tractable in the parameterized sense of the term, and that a simple heuristic is sufficient to make a well-known partial-order planner exploit this fact.

[1]  Malte Helmert,et al.  A Planning Heuristic Based on Causal Graph Analysis , 2004, ICAPS.

[2]  Michael R. Fellows,et al.  Parameterized Complexity , 1998 .

[3]  Bernhard Nebel,et al.  COMPLEXITY RESULTS FOR SAS+ PLANNING , 1995, Comput. Intell..

[4]  Christer Bäckström,et al.  All PSPACE-Complete Planning Problems Are Equal but Some Are More Equal than Others , 2011, SOCS.

[5]  Christer Backstrom,et al.  Computational Complexity of Reasoning about Plans , 1992 .

[6]  Stefan Edelkamp,et al.  Program Model Checking via Action Planning , 2010, MoChArt.

[7]  Krzysztof Pietrzak,et al.  On the parameterized complexity of the fixed alphabet shortest common supersequence and longest common subsequence problems , 2003, J. Comput. Syst. Sci..

[8]  Carmel Domshlak,et al.  New Islands of Tractability of Cost-Optimal Planning , 2008, J. Artif. Intell. Res..

[9]  Ronen I. Brafman,et al.  Strucutre and Complexitiy in Planning with Unary Operators , 2000, PuK.

[10]  Christer Bäckström,et al.  Planning in polynomial time: the SAS‐PUBS class , 1991, Comput. Intell..

[11]  Felix Brandt,et al.  On the Fixed-Parameter Tractability of Composition-Consistent Tournament Solutions , 2011, IJCAI.

[12]  Michael R. Fellows,et al.  The Computer Journal Special Issue on Parameterized Complexity: Foreword by the Guest Editors , 2008, Comput. J..

[13]  Anders Jonsson,et al.  The Complexity of Planning Problems With Simple Causal Graphs , 2008, J. Artif. Intell. Res..

[14]  Stefan Szeider,et al.  Kernels for Global Constraints , 2011, IJCAI.

[15]  Tom Bylander,et al.  The Computational Complexity of Propositional STRIPS Planning , 1994, Artif. Intell..

[16]  Malte Helmert,et al.  The Causal Graph Revisited for Directed Model Checking , 2009, SAS.

[17]  Jörg Flum,et al.  Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series) , 2006 .

[18]  David A. McAllester,et al.  Systematic Nonlinear Planning , 1991, AAAI.

[19]  Michael R. Fellows,et al.  Parameterized complexity: A framework for systematically confronting computational intractability , 1997, Contemporary Trends in Discrete Mathematics.

[20]  Stefan Edelkamp,et al.  Summary of Dagstuhl Seminar 06172 on Directed Model Checking , 2007 .

[21]  Stefan Edelkamp,et al.  06172 Executive Summary -- Directed Model Checking , 2006, Directed Model Checking.

[22]  Malte Helmert,et al.  New Complexity Results for Classical Planning Benchmarks , 2006, ICAPS.

[23]  Stefan Edelkamp,et al.  Taming Numbers and Durations in the Model Checking Integrated Planning System , 2003, PuK.

[24]  J. Hoffmann,et al.  Where 'Ignoring Delete Lists' Works: Local Search Topology in Planning Benchmarks , 2005, J. Artif. Intell. Res..

[25]  Stefan Szeider,et al.  Augmenting Tractable Fragments of Abstract Argumentation , 2011, IJCAI.

[26]  P. Pandurang Nayak,et al.  A Reactive Planner for a Model-based Executive , 1997, IJCAI.

[27]  Christer Backstr.  Planning Using Transformation between Equivalent Formalisms: a Case Study of Eeciency , 1994 .

[28]  Hubie Chen,et al.  Causal graphs and structurally restricted planning , 2010, J. Comput. Syst. Sci..

[29]  Georg Gottlob,et al.  Bounded treewidth as a key to tractability of knowledge representation and reasoning , 2006, Artif. Intell..