A Polynomial Kernel for Funnel Arc Deletion Set
In Directed Feedback Arc Set ( DFAS ) we search for a set of at most k arcs which intersect every cycle in the input digraph. It is a well-known open problem in parameterized complexity to decide if DFAS admits a kernel of polynomial size. We consider C - Arc Deletion Set ( C - ADS ), a variant of D...
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| Vydáno v: | Algorithmica Ročník 84; číslo 8; s. 2358 - 2378 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.08.2022
Springer Nature B.V |
| Témata: | |
| ISSN: | 0178-4617, 1432-0541 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | In
Directed Feedback Arc Set
(
DFAS
) we search for a set of at most
k
arcs which intersect every cycle in the input digraph. It is a well-known open problem in parameterized complexity to decide if
DFAS
admits a kernel of polynomial size. We consider
C
-
Arc Deletion Set
(
C
-
ADS
), a variant of
DFAS
where we want to remove at most
k
arcs from the input digraph in order to turn it into a digraph of a class
C
. In this work, we choose
C
to be the class of
funnels
.
Funnel
-
ADS
is NP-hard even if the input is a DAG, but is fixed-parameter tractable with respect to
k
. So far no polynomial kernels for this problem were known. Our main result is a kernel for
Funnel
-
ADS
with
O
(
k
6
)
many vertices and
O
(
k
7
)
many arcs, computable in
O
(
n
m
)
time, where
n
is the number of vertices and
m
the number of arcs in the input digraph. |
|---|---|
| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0178-4617 1432-0541 |
| DOI: | 10.1007/s00453-022-00960-w |