Sorting, minimal feedback sets, and Hamilton paths in tournaments
SIAM Journal on Discrete Mathematics
On the complexity of blocks-world planning
Artificial Intelligence
Automatically generating abstractions for planning
Artificial Intelligence
State-variable planning under structural restrictions: algorithms and complexity
Artificial Intelligence
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Tractable plan existence does not imply tractable plan generation
Annals of Mathematics and Artificial Intelligence
Complexity results for standard benchmark domains in planning
Artificial Intelligence
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
A note on complete subdivisions in digraphs of large outdegree
Journal of Graph Theory
Non-dichotomies in Constraint Satisfaction Complexity
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Factored planning: how, when, and when not
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
The Causal Graph Revisited for Directed Model Checking
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
A reactive planner for a model-based executive
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Structure and complexity in planning with unary operators
Journal of Artificial Intelligence Research
The fast downward planning system
Journal of Artificial Intelligence Research
The complexity of planning problems with simple causal graphs
Journal of Artificial Intelligence Research
New Islands of tractability of cost-optimal planning
Journal of Artificial Intelligence Research
Planning over chain causal graphs for variables with domains of size 5 Is NP-hard
Journal of Artificial Intelligence Research
The role of macros in tractable planning
Journal of Artificial Intelligence Research
Causal graphs and structurally restricted planning
Journal of Computer and System Sciences
Implicit abstraction heuristics
Journal of Artificial Intelligence Research
The influence of k-dependence on the complexity of planning
Artificial Intelligence
Parameterized Complexity
Limitations of acyclic causal graphs for planning
Artificial Intelligence
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The causal graph of a planning instance is an important tool for planning both in practice and in theory. The theoretical studies of causal graphs have largely analysed the computational complexity of planning for instances where the causal graph has a certain structure, often in combination with other parameters like the domain size of the variables. Chen and Giménez ignored even the structure and considered only the size of the weakly connected components. They proved that planning is tractable if the components are bounded by a constant and otherwise intractable. Their intractability result was, however, conditioned by an assumption from parameterised complexity theory that has no known useful relationship with the standard complexity classes. We approach the same problem from the perspective of standard complexity classes, and prove that planning is NP-hard for classes with unbounded components under an additional restriction we refer to as SP-closed. We then argue that most NP-hardness theorems for causal graphs are difficult to apply and, thus, prove a more general result; even if the component sizes grow slowly and the class is not densely populated with graphs, planning still cannot be tractable unless the polynomial hierachy collapses. Both these results still hold when restricted to the class of acyclic causal graphs. We finally give a partial characterization of the borderline between NP-hard and NP-intermediate classes, giving further insight into the problem.