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 $O(8^kk!*poly(n))$.
@InProceedings{razgon_et_al:DagSemProc.07281.4, author = {Razgon, Igor and O'Sullivan, Barry}, title = {{Directed Feedback Vertex Set is Fixed-Parameter Tractable}}, booktitle = {Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs}, pages = {1--14}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2007}, volume = {7281}, editor = {Erik Demaine and Gregory Z. Gutin and Daniel Marx and Ulrike Stege}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07281.4}, URN = {urn:nbn:de:0030-drops-12363}, doi = {10.4230/DagSemProc.07281.4}, annote = {Keywords: Directed FVS, Multicut, Directed Acyclic Graph (DAG)} }
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