The Complexity of Optimal Monotonic Planning: The Bad, The Good, and The Causal Graph

Domshlak, Carmel; Nazarenko, A. V.

doi:10.1613/jair.4145

Cited by 8 publications

(4 citation statements)

References 48 publications

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“…It is not obvious what other parameter bounds would lead to tractability so it may be easier to consider larger classes of causal graphs than polytrees. The obvious generalisation is to consider causal graphs that have bounded treewidth-this is a method that have led to a large number of tractability results in many different areas of computer science, with a few examples also in planning (Brafman and Domshlak 2006;Domshlak and Nazarenko 2013;Bäckström 2014). The very same planning algorithm would be useful also in this case: it runs in polynomial time whenever the tree-width of the causal graph and the number of variable changes are bounded.…”

Section: Discussionmentioning

confidence: 99%

A Refined Understanding of Cost-Optimal Planning with Polytree Causal Graphs

Bäckström

Jönsson

Ordyniak

2021

SOCS

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Complexity analysis based on the causal graphs of planning instances has emerged as a highly important area of research. In particular, tractability results have led to new methods for the identification of domain-independent heuristics. Important early examples of such tractability results have been presented by, for instance, Brafman & Domshlak and Katz & Keyder. More general results based on polytrees and bounding certain parameters were subsequently derived by Aghighi et al. and Ståhlberg. We continue this line of research by analyzing cost-optimal planning restricted to instances with a polytree causal graph, bounded domain size and bounded depth (i.e. the length of the longest directed path in the causal graph). We show that no further restrictions are necessary for tractability, thus generalizing the previous results. Our approach is based on a novel method of closely analysing optimal plans: we recursively decompose the causal graph in a way that allows for bounding the number of variable changes as a function of the depth, using a reording argument and a comparison with prefix trees of known size. We can then transform the planning instances into constraint satisfaction instances; an idea that has previously been exploited by, for example, Brafman & Domshlak and Bäckström. This allows us to utilise efficient algorithms for constraint optimisation over tree-structured instances.

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Section: Discussionmentioning

confidence: 99%

A Refined Understanding of Cost-Optimal Planning with Polytree Causal Graphs

Bäckström

Jönsson

Ordyniak

2021

SOCS

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“…We explore two kinds of relaxations: one is based on the monotone (also known as "value accumulating") relaxation that generalises the delete relaxation to non-propositional state variables (Gregory et al, 2012;Domshlak & Nazarenko, 2013), and the other on a form of abstraction, namely projection. In both we have relaxed states, which can be viewed as representing sets of assignments to the primary state variables.…”

Section: Relaxations Of Planning With State Constraintsmentioning

confidence: 99%

“…Several researchers (e.g., Gregory et al, 2012;Domshlak & Nazarenko, 2013) have noted that the delete relaxation of propositional planning can also be characterised as planning with a value accumulating interpretation of action effects, instead of the usual value assignment semantics: each state variable, v, in a relaxed state has a set of values instead of just one value, and applying an action effect v := e adds the new value, e, to the set, without removing any existing value.…”

Section: The Monotone Relaxation Of Classical Planningmentioning

confidence: 99%

Extending Classical Planning with State Constraints: Heuristics and Search for Optimal Planning

Haslum¹,

Ivankovic²,

Ramírez³

et al. 2018

jair

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We present a principled way of extending a classical AI planning formalism with systems of state constraints, which relate -sometimes determine -the values of variables in each state traversed by the plan. This extension occupies an attractive middle ground between expressivity and complexity. It enables modelling a new range of problems, as well as formulating more efficient models of classical planning problems. An example of the former is planning-based control of networked physical systems -power networks, for examplein which a local, discrete control action can have global effects on continuous quantities, such as altering flows across the entire network. At the same time, our extension remains decidable as long as the satisfiability of sets of state constraints is decidable, including in the presence of numeric state variables, and we demonstrate that effective techniques for costoptimal planning known in the classical setting -in particular, relaxation-based admissible heuristics -can be adapted to the extended formalism. In this paper, we apply our approach to constraints in the form of linear or non-linear equations over numeric state variables, but the approach is independent of the type of state constraints, as long as there exists a procedure that decides their consistency. The planner and the constraint solver interact through a well-defined, narrow interface, in which the solver requires no specialisation to the planning context. Furthermore, we present an admissible search algorithm -a variant of A -that is able to make use of additional information provided by the search heuristic, in the form of preferred actions. Although preferred actions have been widely used in satisficing planning, we are not aware of any previous use of them in optimal planning.

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“…The Thirty-Seventh AAAI Conference on Artificial Intelligence ning (Brafman and Domshlak 2003;Bäckström and Jonsson 2013;Domshlak and Nazarenko 2013).…”

Section: Introductionmentioning

confidence: 99%

Structurally Restricted Fragments of Numeric Planning – a Complexity Analysis

Shleyfman

Gnad

Jönsson

2023

AAAI

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Numeric planning is known to be undecidable even under severe restrictions. Prior work has investigated the decidability boundaries by restricting the expressiveness of the planning formalism in terms of the numeric functions allowed in conditions and effects. We study a well-known restricted form of Hoffmann's simple numeric planning, which is undecidable. We analyze the complexity by imposing restrictions on the causal structure, exploiting a novel method for bounding variable domain sizes. First, we show that plan existence for tasks where all numeric variables are root nodes in the causal graph is in PSPACE. Second, we show that for tasks with only numeric leaf variables the problem is decidable, and that it is in PSPACE if the propositional state space has a fixed size. Our work lays a strong foundation for future investigations of structurally more complex tasks. From a practical perspective, our method allows to employ heuristics and methods that are geared towards finite variable domains (such as pattern database heuristics or decoupled search) to solve non-trivial families of numeric planning problems.

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The Complexity of Optimal Monotonic Planning: The Bad, The Good, and The Causal Graph

Cited by 8 publications

References 48 publications

A Refined Understanding of Cost-Optimal Planning with Polytree Causal Graphs

A Refined Understanding of Cost-Optimal Planning with Polytree Causal Graphs

Extending Classical Planning with State Constraints: Heuristics and Search for Optimal Planning

Structurally Restricted Fragments of Numeric Planning – a Complexity Analysis

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