A Space-Efficient Algebraic Approach to Robotic Motion Planning
We consider efficient route planning for robots in applications such as infrastructure inspection and automated surgical imaging. These tasks can be modeled via the combinatorial problem Graph Inspection. The best known algorithms for this problem are limited in practice by exponential space complexity. In this paper, we develop a memory-efficient approach using algebraic tools related to monomial testing on the polynomials associated with certain arithmetic circuits. Our contributions are two-fold. We first repair a minor flaw in existing work on monomial detection using a new approach we call tree certificates. We further show that, in addition to detection, these tools allow us to efficiently recover monomials of interest from circuits, opening the door for significantly broadened application of related algebraic tools. For Graph Inspection, we design and evaluate a complete algebraic pipeline. Our engineered implementation demonstrates that circuit-based algorithms are indeed memory-efficient in practice, thus encouraging further engineering efforts.