Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Tight Lower Bound for Edge-Disjoint Paths on Planar DAGs   (see paper for full abstract)
  We show that the Edge-Disjoint Paths problem is W[1]-hard parameterized by
the number $k$ of terminal pairs, even when the input graph is a planar
directed acyclic graph (DAG). This answers a question of Slivkins (ESA '03,
SIDMA '10). Moreover, under the Exponential Time Hypothesis (ETH), we show that
there is no $f(k)\cdot n^{o(k)}$ algorithm for Edge-Disjoint Paths on planar
DAGs, where $k$ is the number of terminal pairs, $n$ is the number of vertices
and $f$ is any computable function. Our hardness holds even if both the maximum
in-degree and maximum out-degree of the graph are at most $2$.
  Our result shows that the $n^{O(k)}$ algorithm of Fortune et al. (TCS '80)
for Edge-Disjoint Paths on DAGs is asymptotically tight, even if we add an
extra restriction of planarity. As a special case of our result, we obtain that
Edge-Disjoint Paths on planar directed graphs is W[1]-hard parameterized by the
number $k$ of terminal pairs. This answers a question of Cygan et al. (FOCS
'13) and Schrijver (pp. 417-444, Building Bridges II, '19), and completes the
landscape of the parameterized complexity status of edge and vertex versions of
the Disjoint Paths problem on planar directed and planar undirected graphs.

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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: econ