Plan Reordering and Parallel Execution — A Parameterized Complexity View

While seminal work has studied the problem of relaxing the ordering of a plan’s actions, less attention has been given to the problem of relaxing and modifying a plan’s variable bindings. This paper studies the problem of relaxing a plan into a partial plan which specifies which operators must be executed, but need not completely specify their order or variable bindings. While partial plans can provide an agent with additional flexibility and robustness at execution time, many operations over partial plans are intractable. This paper tackles this problem by proposing and empirically evaluating a fixed-parameter tractable algorithm which searches for tractable, flexible partial plans.

Section: Discussionmentioning

confidence: 99%

Plan Relaxation via Action Debinding and Deordering

Waters

Nebel

Padgham

et al. 2018

“…POCL plans are particularly attractive for reasoning about plan optimization since causal links explicitly represent the causal relationships between actions (Waters, Padgham, and Sardina 2020;Waters et al 2018;Muise, Beck, and McIlraith 2016). One work investigates the computational hardness for optimizing the action set of a POCL plan (Olz and Bercher 2019), whereas several works investigate the computational hardness of optimizing ordering constraints or execution time (makespan) for partially ordered plans and POCL plans in particular (Bercher and Olz 2020;Aghighi and Bäckström 2017;Bäckström 1998).…”

Section: Related Work On Complexity Studies In Pocl Planningmentioning

confidence: 99%

A Closer Look at Causal Links: Complexity Results for Delete-Relaxation in Partial Order Causal Link (POCL) Planning

Bercher

2021

Partial Order Causal Link (POCL) planning follows the principle of least commitment in that it maintains only a partial order on its actions to prevent unnecessary early commitment during search. This can reduce the search space significantly by systematically representing up to an exponential number of action sequences in just a single search node. Progress on goal achievement is represented fully by this partial order and by causal links, which represent the causal relationships between these actions as well as between the initial state and goal. Plan existence for a state in classical planning thus corresponds to plan existence for a partial plan in POCL planning. Yet almost no theoretical investigations for POCL plan existence were conducted so far. While delete-relaxation makes plan existence tractable in classical planning, we show it to be NP-hard in POCL planning unless the current plan is totally ordered or causal links are almost completely ignored.

“…Some only loosely related work on theoretical investigations of partially ordered plans studied the complexity of finding an executable action linearization under various restrictions (Nebel and Bäckström 1994;Tan and Gruninger 2014), the complexity of finding a solution given a deleterelaxed model (Bercher et al 2013), and the complexity of reordering actions to optimize ordering constraintrelated optimality criteria (Bäckström 1998;Aghighi and Bäckström 2017).…”

Section: Related Workmentioning

confidence: 99%

“…Therefore, we look at the problem again under the light of fixing them as a parameter in the input. This leads to the theory of parameterized complexity, which has been initiated by Downey and Fellows (1999), but we follow the definition of Aghighi and Bäckström (2017).…”

Section: Parameterized Complexitymentioning

confidence: 99%

“…Partially ordered plans are basically a compact representation for a set of total-order plans. Mutually unordered actions can be executed simultaneously allowing to postpone the decision about the exact execution order until runtime, which makes these plans more flexible in time-sensitive applications (Vi-dal and Geffner 2006;Muise, Beck, and McIlraith 2016;Aghighi and Bäckström 2017).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Eliminating Redundant Actions in Partially Ordered Plans — A Complexity Analysis

Olz¹,

Bercher²

2019

In this paper we study the computational complexity of postoptimizing partially ordered plans, i.e., we investigate the problem that is concerned with detecting and deleting unnecessary actions. For totally ordered plans it can easily be tested in polynomial time whether a single action can be removed without violating executability. Identifying an executable subplan, i.e., asking whether k plan steps can be removed, is known to be NP-complete. We investigate the same questions for partially ordered input plans, as they are created by many search algorithms or used by real-world applications – in particular time-critical ones that exploit parallelism of non-conflicting actions. More formally, we investigate the computational complexity of removing an action from a partially ordered solution plan in which every linearization is a solution in the classical sense while allowing ordering insertions afterwards to repair arising executability issues. It turns out that this problem is NP-complete – even if just a single action is removed – and thereby show that this reasoning task is harder than for totally ordered plans. Moreover, we identify the structural properties responsible for this hardness by providing a fixed-parameter tractability (FPT) result.