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Routing Few Robots in a Crowded Network

Authors Argyrios Deligkas , Eduard Eiben , Robert Ganian , Iyad Kanj , Dominik Leko, M. S. Ramanujan

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ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • graph coordinated motion planning
  • parameterized complexity
  • treedepth

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Abstract

In Graph Coordinated Motion Planning, we are given a graph G some of whose vertices are occupied by robots, and we are asked to route k marked robots to their destinations while avoiding collisions and without exceeding a given budget 𝓁 on the number of robot moves. We continue the recent investigation of the problem [ICALP 2024], focusing on the parameter k that captures the task of routing a small number of robots in a possibly crowded graph. We prove that the problem is W[1]-hard parameterized by 𝓁 even for k = 1, but fixed-parameter tractable parameterized by k plus the treedepth of G. We complement the latter algorithm with an NP-hardness reduction which shows that both parameters are necessary to achieve tractability.

Cite As Get BibTex

Argyrios Deligkas, Eduard Eiben, Robert Ganian, Iyad Kanj, Dominik Leko, and M. S. Ramanujan. Routing Few Robots in a Crowded Network. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.20

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
Dominik Leko
  • Algorithms and Complexity Group, TU Wien, IL, Austria
M. S. Ramanujan
  • Department of Computer Science, University of Warwick, UK

Funding

  • Deligkas, Argyrios: UKRI EPSRC grant EP/X039862/1.
  • Ganian, Robert: Projects No. 10.55776/Y1329 and 10.55776/COE12 of the Austrian Science Fund (FWF), Project No. ICT22-029 of the Vienna Science Foundation (WWTF).
  • Kanj, Iyad: DePaul URC Grants 606601 and 350130.
  • Ramanujan, M. S.: Engineering and Physical Sciences Research Council (EPSRC) grant EP/V044621/1.

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