Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-agent Path Planning and Network Flow   This paper connects multi-agent path planning on graphs (roadmaps) to network
flow problems, showing that the former can be reduced to the latter, therefore
enabling the application of combinatorial network flow algorithms, as well as
general linear program techniques, to multi-agent path planning problems on
graphs. Exploiting this connection, we show that when the goals are permutation
invariant, the problem always has a feasible solution path set with a longest
finish time of no more than $n + V - 1$ steps, in which $n$ is the number of
agents and $V$ is the number of vertices of the underlying graph. We then give
a complete algorithm that finds such a solution in $O(nVE)$ time, with $E$
being the number of edges of the graph. Taking a further step, we study time
and distance optimality of the feasible solutions, show that they have a
pairwise Pareto optimal structure, and again provide efficient algorithms for
optimizing two of these practical objectives.

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The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas