Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Technical Report on PLS-Completeness of Single-Swap for Unweighted
  Metric Facility Location and $K$-Means   Recently, [Bra17] showed that the single-swap heuristic for weighted metric
uncapacitated facility location and $K$-Means is tightly PLS-complete. We build
upon this work and present a stronger reduction, which proves tight
PLS-completeness for the unweighted version of both problems.

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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: nucl-th