Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Perimeter Guarding with Heterogeneous Robot Teams: Complexity
  Analysis and Effective Algorithms   We perform structural and algorithmic studies of significantly generalized
versions of the optimal perimeter guarding (OPG) problem. As compared with the
original OPG where robots are uniform, in this paper, many mobile robots with
heterogeneous sensing capabilities are to be deployed to optimally guard a set
of one-dimensional segments. Two complimentary formulations are investigated
where one limits the number of available robots (OPG_LR) and the other seeks to
minimize the total deployment cost (OPG_MC). In contrast to the original OPG
which admits low-polynomial time solutions, both OPG_LR and OPG_MC are
computationally intractable with OPG_LR being strongly NP-hard. Nevertheless,
we develop fairly scalable pseudo-polynomial time algorithms for practical,
fixed-parameter subcase of OPG_LR; we also develop pseudo-polynomial time
algorithm for general OPG_MC and polynomial time algorithm for the
fixed-parameter OPG_MC case. The applicability and effectiveness of selected
algorithms are demonstrated through extensive numerical experiments.

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The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio