3 research outputs found
Directed Feedback Vertex Set is Fixed-Parameter Tractable
We resolve positively a long standing open question regarding the
fixed-parameter tractability of the parameterized Directed Feedback Vertex Set
problem. In particular, we propose an algorithm which solves this problem in
.Comment: 14 page
Almost 2-SAT is Fixed-Parameter Tractable
We consider the following problem. Given a 2-CNF formula, is it possible to
remove at most clauses so that the resulting 2-CNF formula is satisfiable?
This problem is known to different research communities in Theoretical Computer
Science under the names 'Almost 2-SAT', 'All-but- 2-SAT', '2-CNF deletion',
'2-SAT deletion'. The status of fixed-parameter tractability of this problem is
a long-standing open question in the area of Parameterized Complexity. We
resolve this open question by proposing an algorithm which solves this problem
in and thus we show that this problem is fixed-parameter
tractable.Comment: This new version fixes the bug found by Somnath Sikdar in the proof
of Claim 8. In the repaired version the modification of the Almost 2-SAT
problem called 2-SLASAT is no longer needed and only the modification called
2-ASLASAT remains relevant. Hence the whole manuscript is updated so that the
2-SLASAT problem is not mentioned there anymor
Directed Feedback Vertex Set is Fixed-Parameter Tractable
Abstract. We resolve positively a long standing open question regarding the fixed-parameter tractability of the parameterized Directed Feedback Vertex Set problem. In particular, we propose an algorithm which solves this problem in O(8 k k! ∗ poly(n)). Keywords. Directed Feedback Vertex Set, Fixed-Parameter Tractability