The Complexity of Planning Problems With Simple Causal Graphs

TL;DR

This paper investigates the computational complexity of planning problems with simple causal graphs, providing new polynomial-time algorithms and complexity hardness results for various classes.

Contribution

It introduces a polynomial-time macro-based planning algorithm for acyclic causal graphs and establishes NP-hardness and NP-completeness results for other classes.

Findings

Polynomial-time plan generation for 3S planning problems.

NP-hardness of plan existence with multi-valued variables and chain causal graphs.

NP-completeness of plan existence with binary variables and polytree causal graphs.

Abstract

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.