The Complexity of Planning Revisited - A Parameterized Analysis

TL;DR

This paper revisits the computational complexity of planning problems using parameterized complexity analysis, revealing new tractability results and explaining practical simplicity of certain planning cases.

Contribution

It applies parameterized complexity to planning subclasses, providing new separation results and practical insights into tractability.

Findings

Certain planning restrictions are fixed-parameter tractable.

A simple heuristic improves partial-order planner performance.

New separation results clarify complexity landscape.

Abstract

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.