Complexity of planning for connected agents

Abstract

We study a variant of the multi-agent path finding (MAPF) problem in which the group of agents are required to stay connected with a supervising base station throughout the execution. In addition, we consider the problem of covering an area with the same connectivity constraint. We show that both problems are PSPACE-complete on directed and undirected topological graphs while checking the existence of a bounded plan is NP-complete when the bound is given in unary (and PSPACE-hard when the encoding is in binary). Moreover, we identify a realistic class of topological graphs on which the decision problem falls in NLOGSPACE although the bounded versions remain NP-complete for unary encoding.

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Notes

  1. 1.

    The bounded plan is clearly in NP when the bound \(\ell\) is written in unary: simply guess a solution of length at most \(\ell\) and check that it is correct. When the bound is given in binary, a solution may be in exponential size, and cannot be guessed in polynomial time.

  2. 2.

    Their reduction is from a problem called the reconfiguration problem on constraint graphs. The topological graph computed from a constraint graph contains single nodes ( ), paths of length 3 (which we denote by ) and a single path graph of length |E| (denoted by ), with E the set of edges in the constraint graph.

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Acknowledgements

This work was partially supported by UAV Retina Funded by EIT Digital. Special thanks to François Bodin for initiating the idea of this work. We thank Eva Soulier for the provided work during her internship. We also thank Sophie Pinchinat for useful comments.

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Correspondence to Arthur Queffelec.

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Charrier, T., Queffelec, A., Sankur, O. et al. Complexity of planning for connected agents. Auton Agent Multi-Agent Syst 34, 44 (2020). https://doi.org/10.1007/s10458-020-09468-5

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Keywords

  • Artifical intelligence
  • Multi-agent systems
  • Planning
  • Computational complexity

Mathematics Subject Classification

  • 68T20
  • 03D15