Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Multi-Robot Path Planning on Graphs: Structure and Computational
  Complexity   We study the problem of optimal multi-robot path planning on graphs (MPP)
over four distinct minimization objectives: the total arrival time, the
makespan (last arrival time), the total distance, and the maximum (single-robot
traveled) distance. On the structure side, we show that each pair of these four
objectives induces a Pareto front and cannot always be optimized
simultaneously. Then, through reductions from 3-SAT, we further establish that
computation over each objective is an NP-hard task, providing evidence that
solving MPP optimally is generally intractable. Nevertheless, in a related
paper, we design complete algorithms and efficient heuristics for optimizing
all four objectives, capable of solving MPP optimally or near-optimally for
hundreds of robots in challenging setups.

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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: math
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom