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arXiv · 2001.04311

Lower Bounds for Shoreline Searching with 2 or More Robots

Sumi Acharjee·Konstantinos Georgiou·Somnath Kundu·Akshaya Srinivasan
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Abstract

Searching for a line on the plane with $n$ unit speed robots is a classic online problem that dates back to the 50's, and for which competitive ratio upper bounds are known for every $n\geq 1$. In this work we improve the best lower bound known for $n=2$ robots from 1.5993 to 3. Moreover we prove that the competitive ratio is at least $\sqrt{3}$ for $n=3$ robots, and at least $1/\cos(\pi/n)$ for $n\geq 4$ robots. Our lower bounds match the best upper bounds known for $n\geq 4$, hence resolving these cases. To the best of our knowledge, these are the first lower bounds proven for the cases $n\geq 3$ of this several decades old problem.

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Sumi Acharjee, Konstantinos Georgiou, Somnath Kundu, Akshaya Srinivasan. 2020-01-13. Lower Bounds for Shoreline Searching with 2 or More Robots. https://arxiv.org/abs/2001.04311

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