Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmless Sets in Sparse Classes   In the classic TARGET SAT SELECTION problem, we are asked to minimise the
number of nodes to activate so that, after the application of a certain
propagation process, all nodes of the graph are active. Bazgan and Chopin
[Discrete Optimization}, 14:170--182, 2014] introduced the opposite problem,
named HARMLESS SET, in which they ask to maximise the number of nodes to
activate such that not a single additional node is activated. In this paper we
investigate how sparsity impacts the tractability of HARMLESS SET.
Specifically, we answer two open questions posed by the aforementioned authors,
namely a) whether the problem is FPT on planar graphs and b) whether it is FPT
parametrised by treewidth. The first question can be answered in the positive
using existing meta-theorems on sparse classes, and we further show that
HARMLESS SET not only admits a polynomial kernel, but that it can be solved in
subexponential time.
  We then answer the second question in the negative by showing that the
problem is W[1]-hard when parametrised by a parameter that upper bounds
treewidth.

26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con