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Hardness of Traversing Gadget Systems with Small Bandwidth

Authors MIT Gadgets Group, Erik D. Demaine , Jenny Diomidova, Timothy Gomez, Markus Hecher , Jayson Lynch

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Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Abstract machines
  • Theory of computation → Turing machines
Keywords
  • Gadgets
  • Motion Planning
  • Parameterized Complexity
  • Hardness

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Abstract

The motion-planning-through-gadgets framework has enabled proofs of PSPACE-completeness for many motion-planning problems, ranging from swarm and modular robotics to DNA computing to video games. In this paper, we strengthen this framework to show that, for several useful gadgets and gadget families, motion planning remains PSPACE-complete even when gadgets are connected together into a graph of constant bandwidth (which implies constant pathwidth, treewidth, and cliquewidth). We then show how this result applies to several geometric/grid-based motion-planning problems, establishing PSPACE-completeness even when restricted to a rectangle/box where only one dimension is large (superconstant). On the positive side, we find one family of gadgets (DAG gadgets) for which motion planning is fixed-parameter tractable with respect to bandwidth.

Cite As Get BibTex

MIT Gadgets Group, Erik D. Demaine, Jenny Diomidova, Timothy Gomez, Markus Hecher, and Jayson Lynch. Hardness of Traversing Gadget Systems with Small Bandwidth. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SAND.2025.11

Author Details

MIT Gadgets Group
  • Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA
Erik D. Demaine
  • Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA
Jenny Diomidova
  • Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA
Timothy Gomez
  • Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA
Markus Hecher
  • Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA
Jayson Lynch
  • Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA

Funding

This research was funded by the Austrian Science Fund (FWF), grants J 4656 and P 32830, as well as the Society for Research Funding in Lower Austria (GFF) grant ExzF-0004.

References

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