Multi-agent Pathfinding with n Agents on Graphs with n Vertices: Combinatorial Classification and Tight Algorithmic Bounds

  • Klaus-Tycho Foerster
  • Linus Groner
  • Torsten Hoefler
  • Michael Koenig
  • Sascha Schmid
  • Roger Wattenhofer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10236)


We investigate the multi-agent pathfinding (MAPF) problem with n agents on graphs with n vertices: Each agent has a unique start and goal vertex, with the objective of moving all agents in parallel movements to their goal s.t. each vertex and each edge may only be used by one agent at a time. We give a combinatorial classification of all graphs where this problem is solvable in general, including cases where the solvability depends on the initial agent placement.

Furthermore, we present an algorithm solving the MAPF problem in our setting, requiring \(\mathcal {O}(n^2)\) rounds, or \(\mathcal {O}(n^3)\) moves of individual agents. Complementing these results, we show that there are graphs where \(\Omega (n^2)\) rounds and \(\Omega (n^3)\) moves are required for any algorithm.


Permutation Group Full Version Combinatorial Condition Label Problem Agent Move 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We would like to thank the anonymous reviewers for their helpful comments. Klaus-Tycho Foerster is supported by the Danish Villum Foundation.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Klaus-Tycho Foerster
    • 2
  • Linus Groner
    • 1
  • Torsten Hoefler
    • 1
  • Michael Koenig
    • 1
  • Sascha Schmid
    • 1
  • Roger Wattenhofer
    • 1
  1. 1.ETH ZurichZurichSwitzerland
  2. 2.Aalborg UniversityAalborgDenmark

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