A Structural Complexity Analysis of Hierarchical Task Network Planning

2024-01-25

AI Summary

This paper systematically investigates the computational complexity of three fundamental problems in Hierarchical Task Network (HTN) planning: plan verification, executability checking, and state reachability. Using structured graph-theoretic modeling, parameterized algorithm design, and tight lower-bound constructions, it establishes the first complete W[1]/FPT classification of these problems under standard parameters. It introduces the first meta-theorem that lifts polynomial-time solvability from primitive task networks to general task networks, and proves the tightness of its preconditions. Furthermore, for natural classes of primitive networks, it derives new polynomial-time algorithms for all three problems and provides matching conditional lower bounds. These results constitute a systematic breakthrough in HTN complexity theory, enabling principled complexity transfer across HTN formalisms and unifying previously fragmented analyses.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Planning under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We perform a refined complexity-theoretic analysis of three classical problems in the context of Hierarchical Task Network Planning: the verification of a provided plan, whether an executable plan exists, and whether a given state can be reached. Our focus lies on identifying structural properties which yield tractability. We obtain new polynomial algorithms for all three problems on a natural class of primitive networks, along with corresponding lower bounds. We also obtain an algorithmic meta-theorem for lifting polynomial-time solvability from primitive to general task networks, and prove that its preconditions are tight. Finally, we analyze the parameterized complexity of the three problems.

Problem

• Analyzing complexity of Hierarchical Task Network plan verification
• Determining existence of executable plans in HTN planning
• Investigating structural properties for tractable reachability analysis

Innovation

• Polynomial algorithms for primitive networks
• Meta-theorem for tractability lifting
• Parameterized complexity analysis applied