41,416 research outputs found
The Complexity of Planning Problems With Simple Causal Graphs
We present three new complexity results for classes of planning problems with
simple causal graphs. First, we describe a polynomial-time algorithm that uses
macros to generate plans for the class 3S of planning problems with binary
state variables and acyclic causal graphs. This implies that plan generation
may be tractable even when a planning problem has an exponentially long minimal
solution. We also prove that the problem of plan existence for planning
problems with multi-valued variables and chain causal graphs is NP-hard.
Finally, we show that plan existence for planning problems with binary state
variables and polytree causal graphs is NP-complete
Structure and Complexity in Planning with Unary Operators
Unary operator domains -- i.e., domains in which operators have a single
effect -- arise naturally in many control problems. In its most general form,
the problem of STRIPS planning in unary operator domains is known to be as hard
as the general STRIPS planning problem -- both are PSPACE-complete. However,
unary operator domains induce a natural structure, called the domain's causal
graph. This graph relates between the preconditions and effect of each domain
operator. Causal graphs were exploited by Williams and Nayak in order to
analyze plan generation for one of the controllers in NASA's Deep-Space One
spacecraft. There, they utilized the fact that when this graph is acyclic, a
serialization ordering over any subgoal can be obtained quickly. In this paper
we conduct a comprehensive study of the relationship between the structure of a
domain's causal graph and the complexity of planning in this domain. On the
positive side, we show that a non-trivial polynomial time plan generation
algorithm exists for domains whose causal graph induces a polytree with a
constant bound on its node indegree. On the negative side, we show that even
plan existence is hard when the graph is a directed-path singly connected DAG.
More generally, we show that the number of paths in the causal graph is closely
related to the complexity of planning in the associated domain. Finally we
relate our results to the question of complexity of planning with serializable
subgoals
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+ (Baeckstroem 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.Comment: (author's self-archived copy
- …