Parameterized Complexity Results for Plan Reuse

TL;DR

This paper analyzes the computational complexity of plan reuse in case-based planning using parameterized complexity theory, identifying conditions under which plan reuse is efficiently solvable.

Contribution

It provides a detailed parameterized complexity analysis of plan reuse problems, revealing tractable cases based on structural input parameters.

Findings

Certain plan reuse problems are fixed-parameter tractable under specific restrictions.

The complexity landscape of plan reuse varies significantly with different parameters.

Theoretical results guide practical heuristics for case-based planning.

Abstract

Planning is a notoriously difficult computational problem of high worst-case complexity. Researchers have been investing significant efforts to develop heuristics or restrictions to make planning practically feasible. Case-based planning is a heuristic approach where one tries to reuse previous experience when solving similar problems in order to avoid some of the planning effort. Plan reuse may offer an interesting alternative to plan generation in some settings. We provide theoretical results that identify situations in which plan reuse is provably tractable. We perform our analysis in the framework of parameterized complexity, which supports a rigorous worst-case complexity analysis that takes structural properties of the input into account in terms of parameters. A central notion of parameterized complexity is fixed-parameter tractability which extends the classical notion of polynomial-time tractability by utilizing the effect of structural properties of the problem input. We draw a detailed map of the parameterized complexity landscape of several variants of problems that arise in the context of case-based planning. In particular, we consider the problem of reusing an existing plan, imposing various restrictions in terms of parameters, such as the number of steps that can be added to the existing plan to turn it into a solution of the planning instance at hand.