Next:
GT10 MAXIMUM TRIANGLE
Up:
Covering and Partitioning
Previous:
GT8 MINIMUM FEEDBACK
-
I
NSTANCE
:
Directed graph
.
-
S
OLUTION
:
A feedback arc set, i.e., a subset
such that
A'
contains at least one arc from every directed cycle in
G
.
-
M
EASURE
:
Cardinality of the feedback arc set, i.e.,
|A'|
.
-
Good News:
Approximable within
[
99
].
-
Bad News:
A
PX
-hard [
200
].
-
Comment:
Transformation from M
INIMUM
F
EEDBACK
V
ERTEX
S
ET
[
99
].
The generalized variation in which the input is extended with a subset
S
of vertices and arcs, and the problem is to find an arc set that
contains at least one arc from every directed cycle that intersects
S
,
is approximable within
[
99
].
All these problems are approximable within 9/4 for planar graphs
[
136
].
The constrained variation in which the input is extended with a positive
integer
k
and a subset
S
of
A
, and the problem is to find the feedback
arc set of size
k
that contains the largest number of arcs from
S
,
is not approximable within
for some
[
352
].
The complementary problem of finding the maximum set of arcs
A'
such that
is acyclic is approximable within
where
is the maximum degree
[
44
] and [
161
], it is A
PX
-complete
[
284
],
and if
it admits a PTAS [
23
].
-
Garey and Johnson:
GT8
Viggo Kann
Mon Apr 21 13:07:14 MET DST 1997