The classical NP–hard
feedback arc set problem
(FASP) and
feedback vertex set problem
(FVSP) ask for a minimum set of arcs ε ⊆
E
or vertices ν ⊆
V
whose removal
G
∖ ε,
G
∖ ν makes a given multi–digraph
G
=(
V
,
E
) acyclic, respectively. Though both problems are known to be APX–hard, constant ratio approximations or proofs of inapproximability are unknown. We propose a new universal
O
(|
V
||
E
|
4
)–heuristic for the directed FASP. While a ratio of
r
≈ 1.3606 is known to be a lower bound for the APX–hardness, at least by empirical validation we achieve an approximation of
r
≤ 2. Most of the relevant applications, such as
circuit testing
, ask for solving the FASP on large sparse graphs, which can be done efficiently within tight error bounds with our approach.