Complexity of action path finding with small precondition sets

Peter Damaschke; Karinne Ramirez-Amaro

doi:10.1016/j.dam.2025.12.009

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Complexity of action path finding with small precondition sets

https://doi.org/10.1016/j.dam.2025.12.009

Complexity of action path finding with small precondition sets

Mar 1, 2026
Discrete Applied Mathematics
Peter Damaschke +1 more

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Abstract

Suppose that we are given a finite set of Boolean attributes and a set of actions defined on them. Every action has the effect of changing some attribute values and may also depend on further attribute values which are, however, not changed. The subset of attributes affected by an action is known as precondition. The goal is to find some sequence of executable actions that transform a given initial state into a desired target state. This type of problem appears, e.g., in robot motion planning. In this paper, we study cases of the problem where the precondition of every action only depends on a conjunction of terms with at most two attributes. We classify a number of cases as polynomial-time solvable or NP-complete. They amount to extended versions of some classic graph problems, among them topological orderings and perfect matchings. This appears to be the first systematic study of preconditions, despite the rich literature on many aspects of path finding in finite state spaces. A complete dichotomy of polynomial-time and NP-complete cases remains an open question.

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A novel path planning algorithm based on twofold interpolations

Aug 01, 2008
Zhiwei Liang + 2 more +2

Most grid-based path planners use discrete state transitions that artificially constrain a robot's motion to a small set of possible headings to increments of 45 degrees. Consequently, even ldquooptimalrdquo grid-based path planning algorithms produce unnatural and suboptimal paths. In order to handle the problem, we present a twofold-interpolation-based path planning algorithm called T* for producing low-cost paths through uniform resolution grids. First, it starts at the goal node and propagates through four adjacent nodes, assigning monotonically increasing values to nodes using FMM (fast marching method) interpolation. Consequently, we obtain a goal-propagation map that is zero at the goal node and monotonically increasing along wavefront propagation from the goal node. Subsequently, it begins from robot's position and uses linear interpolation to generate near-optimal paths which eliminate unnecessary turnings. The experimental results demonstrate the performance of our approach.