TY - UNPB
T1 - Patrolling Grids with a Bit of Memory
AU - Amir, Michael
AU - Rabinovich, Dmitry
AU - Bruckstein, Alfred M.
N1 - Publisher: arXiv Version Number: 1
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - 05A99
KW - Combinatorics (math.CO)
KW - Computational Geometry (cs.CG)
KW - Discrete Mathematics (cs.DM)
KW - F.2.2
KW - FOS: Computer and information sciences
KW - FOS: Mathematics
KW - G.2.1
KW - Multiagent Systems (cs.MA)
KW - Robotics (cs.RO)
U2 - https://doi.org/10.48550/ARXIV.2307.09214
DO - https://doi.org/10.48550/ARXIV.2307.09214
M3 - نسخة اولية
T3 - arXiv preprint arXiv:2307.09214
BT - Patrolling Grids with a Bit of Memory
ER -