Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sub-1.5 Time-Optimal Multi-Robot Path Planning on Grids in Polynomial
  Time   Graph-based multi-robot path planning (MRPP) is NP-hard to optimally solve.
In this work, we propose the first low polynomial-time algorithm for MRPP
achieving 1--1.5 asymptotic optimality guarantees on solution makespan for
random instances under very high robot density. Specifically, on an $m_1\times
m_2$ gird, $m_1 \ge m_2$, our RTH (Rubik Table with Highways) algorithm
computes solutions for routing up to $\frac{m_1m_2}{3}$ robots with uniformly
randomly distributed start and goal configurations with a makespan of $m_1 +
2m_2 + o(m_1)$, with high probability. Because the minimum makespan for such
instances is $m_1 + m_2 - o(m_1)$, also with high probability, RTH guarantees
$\frac{m_1+2m_2}{m_1+m_2}$ optimality as $m_1 \to \infty$ for random instances
with up to $\frac{1}{3}$ robot density, with high probability.
$\frac{m_1+2m_2}{m_1+m_2} \in (1, 1.5]$.
  Alongside the above-mentioned key result, we also establish: (1) for
completely filled grids, i.e., $m_1m_2$ robots, any MRPP instance may be solved
in polynomial time under a makespan of $7m_1 + 14m_2$, (2) for
$\frac{m_1m_2}{3}$ robots, RTH solves arbitrary MRPP instances with makespan of
$3m_1+4m_2 + o(m_1)$, (3) for $\frac{m_1m_2}{2}$ robots, a variation of RTH
solves a random MRPP instance with the same 1-1.5 optimality guarantee, and (4)
the same $\frac{m_1+2m_2}{m_1+m_2}$ optimality guarantee holds for regularly
distributed obstacles at $\frac{1}{9}$ density together with
$\frac{2m_1m_2}{9}$ randomly distributed robots; such settings directly map to
real-world parcel sorting scenarios.
  In extensive numerical evaluations, RTH and its variants demonstrate
exceptional scalability as compared with methods including ECBS and DDM,
scaling to over $450 \times 300$ grids with $45,000$ robots, and consistently
achieves makespan around $1.5$ optimal or better, as predicted by our
theoretical analysis.

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The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: math
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th