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• W3048010228 abstract "Given a graph $G = (V,E)$, $A subseteq V$, and integers $k$ and $ell$, the textsc{$(A,ell)$-Path Packing} problem asks to find $k$ vertex-disjoint paths of length $ell$ that have endpoints in $A$ and internal points in $V setminus A$. We study the parameterized complexity of this problem with parameters $|A|$, $ell$, $k$, treewidth, pathwidth, and their combinations. We present sharp complexity contrasts with respect to these parameters. Among other results, we show that the problem is polynomial-time solvable when $ell le 3$, while it is NP-complete for constant $ell ge 4$. We also show that the problem is W[1]-hard parameterized by pathwidth${}+|A|$, while it is fixed-parameter tractable parameterized by treewidth${}+ell$." @default.
• W3048010228 created "2020-08-13" @default.
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• W3048010228 date "2020-08-08" @default.
• W3048010228 modified "2023-10-08" @default.
• W3048010228 title "Parameterized Complexity of $(A,ell)$-Path Packing" @default.
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• W3048010228 hasPublicationYear "2020" @default.
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