Patrolling Grids with a Bit of Memory

Michael Amir, Dmitry Rabinovich, Alfred M. Bruckstein

Research output: Working paperPreprint

Abstract

We study the following problem in elementary robotics: can a mobile agent with b bits of memory, which is able to sense only locations at Manhattan distance V or less from itself, patrol a d-dimensional grid graph? We show that it is impossible to patrol some grid graphs with 0 bits of memory, regardless of V, and give an exact characterization of those grid graphs that can be patrolled with 0 bits of memory and visibility range V. On the other hand, we show that, surprisingly, an algorithm exists using 1 bit of memory and V=1 that patrols any d-dimensional grid graph.
Original languageUndefined/Unknown
DOIs
StatePublished - 2023

Publication series

NamearXiv preprint arXiv:2307.09214

Keywords

  • 05A99
  • Combinatorics (math.CO)
  • Computational Geometry (cs.CG)
  • Discrete Mathematics (cs.DM)
  • F.2.2
  • FOS: Computer and information sciences
  • FOS: Mathematics
  • G.2.1
  • Multiagent Systems (cs.MA)
  • Robotics (cs.RO)

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