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  • 1.
    Aghighi, Meysam
    et al.
    Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering.
    Bäckström, Christer
    Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering.
    A Multi-parameter Complexity Analysis of Cost-optimal and Net-benefit Planning2016In: Twenty-Sixth International Conference on Automated Planning and Scheduling King's College, London June 12, 2016 – June 17, 2016 / [ed] Amanda Coles, Andrew Coles, Stefan Edelkamp, Daniele Magazzeni, Scott Sanner, AAAI Press, 2016, p. 2-10Conference paper (Refereed)
    Abstract [en]

    Aghighi and Bäckström have previously studied cost-optimal planning (COP) and net-benefit planning (NBP) for three action cost domains: the positive integers (Z_+), the non-negative integers (Z_0) and the positive rationals (Q_+). These were indistinguishable under standard complexity analysis for both problems, but separated for COP using parameterised complexity analysis. With the plan cost, k, as parameter, COP was W[2]-complete for Z_+, but para-NP-hard for both Z_0 and Q_+, i.e. presumably much harder. NBP was para-NP-hard for all three domains, thus remaining unseparable. We continue by considering combinations with several additional parameters and also the non-negative rationals (Q_0). Examples of new parameters are the plan length, l, and the largest denominator of the action costs, d. Our findings include: (1) COP remains W[2]-hard for all domains, even if combining all parameters; (2) COP for Z_0 is in W[2] for the combined parameter {k,l}; (3) COP for Q_+ is in W[2] for {k,d} and (4) COP for Q_0 is in W[2] for {k,d,l}. For NBP we consider further additional parameters, where the most crucial one for reducing complexity is the sum of variable utilities. Our results help to understand the previous results, eg. the separation between Z_+ and Q_+ for COP, and to refine the previous connections with empirical findings.

  • 2.
    Aghighi, Meysam
    et al.
    Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering.
    Bäckström, Christer
    Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering.
    Cost-optimal and Net-benefit Planning: A Parameterised Complexity View2015In: 24th International Joint Conference on Artificial Intelligence (IJCAI-15), IJCAI-INT JOINT CONF ARTIF INTELL, ALBERT-LUDWIGS UNIV FREIBURG GEORGES-KOHLER-ALLEE, INST INFORMATIK, GEB 052, FREIBURG, D-79110, GERMANY , 2015, p. 1487-1493Conference paper (Refereed)
    Abstract [en]

    Cost-optimal planning (COP) uses action costs and asks for a minimum-cost plan. It is sometimes assumed that there is no harm in using actions with zero cost or rational cost. Classical complexity analysis does not contradict this assumption; planning is PSPACE-complete regardless of whether action costs are positive or non-negative, integer or rational. We thus apply parameterised complexity analysis to shed more light on this issue. Our main results are the following. COP is W[2]-complete for positive integer costs, i.e. it is no harder than finding a minimum-length plan, but it is para-NPhard if the costs are non-negative integers or positive rationals. This is a very strong indication that the latter cases are substantially harder. Net-benefit planning (NBP) additionally assigns goal utilities and asks for a plan with maximum difference between its utility and its cost. NBP is para-NP-hard even when action costs and utilities are positive integers, suggesting that it is harder than COP. In addition, we also analyse a large number of subclasses, using both the PUBS restrictions and restricting the number of preconditions and effects.

  • 3.
    Aghighi, Meysam
    et al.
    Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, The Institute of Technology.
    Jonsson, Peter
    Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, The Institute of Technology.
    Oversubscription planning: Complexity and compilability2014In: Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, AI Access Foundation , 2014, Vol. 3, p. 2221-2227Conference paper (Refereed)
    Abstract [en]

    Many real-world planning problems are oversubscription problems where all goals are not simultaneously achievable and the planner needs to find a feasible subset. We present complexity results for the so-called partial satisfaction and net benefit problems under various restrictions; this extends previous work by van den Briel et al. Our results reveal strong connections between these problems and with classical planning. We also present a method for efficiently compiling oversubscription problems into the ordinary plan existence problem; this can be viewed as a continuation of earlier work by Keyder and Geffner.

  • 4.
    Aghighi, Meysam
    et al.
    Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, The Institute of Technology.
    Jonsson, Peter
    Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, The Institute of Technology.
    Ståhlberg, Simon
    Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, The Institute of Technology.
    Tractable Cost-Optimal Planning over Restricted Polytree Causal Graphs2015In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, AAAI Press, 2015Conference paper (Refereed)
    Abstract [en]

    Causal graphs are widely used to analyze the complexity of planning problems. Many tractable classes have been identified with their aid and state-of-the-art heuristics have been derived by exploiting such classes. In particular, Katz and Keyder have studied causal graphs that are hourglasses (which is a generalization of forks and inverted-forks) and shown that the corresponding cost-optimal planning problem is tractable under certain restrictions. We continue this work by studying polytrees (which is a generalization of hourglasses) under similar restrictions. We prove tractability of cost-optimal planning by providing an algorithm based on a novel notion of variable isomorphism. Our algorithm also sheds light on the k-consistency procedure for identifying unsolvable planning instances. We speculate that this may, at least partially, explain why merge-and-shrink heuristics have been successful for recognizing unsolvable instances.

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