Parameterized Complexity of (A,ℓ)-Path Packing
Given a graph G = ( V , E ) , A ⊆ V , and integers k and ℓ , the ( A , ℓ ) -Path Packing problem asks to find k vertex-disjoint paths of length exactly ℓ that have endpoints in A and internal points in V \ A . We study the parameterized complexity of this problem with parameters | A |, ℓ , k , treew...
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Published in | Algorithmica Vol. 84; no. 4; pp. 871 - 895 |
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Main Authors | , , , , , , , , |
Format | Journal Article |
Language | English |
Published |
New York
Springer US
01.04.2022
Springer Nature B.V Springer Verlag |
Subjects | |
Online Access | Get full text |
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Summary: | Given a graph
G
=
(
V
,
E
)
,
A
⊆
V
, and integers
k
and
ℓ
, the
(
A
,
ℓ
)
-Path Packing
problem asks to find
k
vertex-disjoint paths of length exactly
ℓ
that have endpoints in
A
and internal points in
V
\
A
. We study the parameterized complexity of this problem with parameters |
A
|,
ℓ
,
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
ℓ
≤
3
, while it is NP-complete for constant
ℓ
≥
4
. We also show that the problem is W[1]-hard parameterized by pathwidth
+
|
A
|
, while it is fixed-parameter tractable parameterized by treewidth
+
ℓ
. Additionally, we study a variant called
Short
A
-Path Packing
that asks to find
k
vertex-disjoint paths of length
at most
ℓ
. We show that all our positive results on the exact-length version can be translated to this version and show the hardness of the cases where |
A
| or
ℓ
is a constant. |
---|---|
ISSN: | 0178-4617 1432-0541 |
DOI: | 10.1007/s00453-021-00875-y |