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Coordinated Motion Planning Is FPT on Discretized Simple Polygons

Authors Argyrios Deligkas , Eduard Eiben , Robert Ganian , Iyad Kanj

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LIPIcs.ICALP.2026.75.pdf
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ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • coordinated motion planning
  • multi-agent path finding
  • parameterized complexity

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Abstract

In the coordinated motion planning problem, we are given a graph together with the starting and destination vertices of k robots. At each time step, any subset of robots may move, each traversing an edge of the graph, provided that no two robots collide. The goal is to compute a schedule that routes all robots to their destinations while minimizing some objective function. In this paper, we focus on the well-studied objective of minimizing the total travel length of all robots. This problem is known to be NP-hard, and it has been shown to be fixed-parameter tractable (FPT), when parameterized by the number k of robots, on full grids (SoCG 2023) and on bounded-treewidth graphs (ICALP 2024). 
We present a fixed-parameter algorithm for coordinated motion planning, parameterized by the number k of robots, on graphs arising from discretizations of simple polygons. Such graphs are of particular interest in real-world applications, where planar motion is often constrained to discretized representations of polygonal environments. Moreover, these graphs generalize rectangular grids; consequently, our result constitutes a significant step toward resolving the parameterized complexity of coordinated motion planning on subgrids and, ultimately, planar graphs - two prominent open problems in the field.

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Argyrios Deligkas, Eduard Eiben, Robert Ganian, and Iyad Kanj. Coordinated Motion Planning Is FPT on Discretized Simple Polygons. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 75:1-75:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.75

Author Details

Argyrios Deligkas
  • Department of Computer Science, Royal Holloway, University of London, Egham, UK
Eduard Eiben
  • Department of Computer Science, Royal Holloway, University of London, Egham, UK
Robert Ganian
  • Algorithms and Complexity Group, TU Wien, Austria
Iyad Kanj
  • School of Computing, DePaul University, Chicago, IL, USA

Funding

  • Deligkas, Argyrios: Supported by Engineering and Physical Sciences Research Council (EPSRC) grant EP/X039862/1.
  • Eiben, Eduard: Supported by Engineering and Physical Sciences Research Council (EPSRC) grant UKRI4530: Exploring Parameterized Complexity in Blockchain Systems.
  • Ganian, Robert: Project No. Y1329 of the Austrian Science Fund (FWF), Project No. ICT22-029 of the Vienna Science Foundation (WWTF).
  • Kanj, Iyad: DePaul URC Grants 606601 and 350130.

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