Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group Control for Procedural Rules: Parameterized Complexity and
  Consecutive Domains   We consider {\sc{Group Control by Adding Individuals}} (\sc{GCAI}) for two
procedural rules -- the consensus-start-respecting rule and the
liberal-start-respecting rule. It is known that {\sc{GCAI}} for both rules are
NP-hard, but whether they are fixed-parameter tractable with respect to the
number of distinguished candidates remained open. We resolve both open problems
in the affirmative. In addition, we strengthen the NP-hardness of GCAI by
showing that, with respect to the natural parameter the number of added
individuals, GCAI for both rules is W[2]-hard. Notably, the W[2]-hardness for
the liberal-start-respecting rule holds even when restricted to a very special
case where the qualifications of individuals satisfy the so-called consecutive
ones property. However, for the consensus-start-respecting rule, the problem
becomes polynomial-time solvable in this special case. We also study a duality
restriction where the disqualifications of individuals fulfill the consecutive
ones property, and we show that under this restriction {\sc{GCAI}} for both
rules turn out to be polynomial-time solvable. Our reductions for showing
W[2]-hardness also imply several other lower bounds concerning kernelization
and exact algorithms.

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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: math
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph