Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover

Authors Sebastian Angrick, Ben Bals, Katrin Casel , Sarel Cohen , Tobias Friedrich , Niko Hastrich , Theresa Hradilak, Davis Issac , Otto Kißig , Jonas Schmidt, Leo Wendt

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Sebastian Angrick
  • Hasso Plattner Institute, Universität Potsdam, Germany
Ben Bals
  • Hasso Plattner Institute, Universität Potsdam, Germany
Katrin Casel
  • Humboldt-Universität zu Berlin, Germany
Sarel Cohen
  • The Academic College of Tel Aviv-Yaffo, Israel
Tobias Friedrich
  • Hasso Plattner Institute, Universität Potsdam, Germany
Niko Hastrich
  • Hasso Plattner Institute, Universität Potsdam, Germany
Theresa Hradilak
  • Hasso Plattner Institute, Universität Potsdam, Germany
Davis Issac
  • Hasso Plattner Institute, Universität Potsdam, Germany
Otto Kißig
  • Hasso Plattner Institute, Universität Potsdam, Germany
Jonas Schmidt
  • Hasso Plattner Institute, Universität Potsdam, Germany
Leo Wendt
  • Hasso Plattner Institute, Universität Potsdam, Germany

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Sebastian Angrick, Ben Bals, Katrin Casel, Sarel Cohen, Tobias Friedrich, Niko Hastrich, Theresa Hradilak, Davis Issac, Otto Kißig, Jonas Schmidt, and Leo Wendt. Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


In the Directed Feedback Vertex Set (DFVS) problem, one is given a directed graph G = (V,E) and wants to find a minimum cardinality set S ⊆ V such that G-S is acyclic. DFVS is a fundamental problem in computer science and finds applications in areas such as deadlock detection. The problem was the subject of the 2022 PACE coding challenge. We develop a novel exact algorithm for the problem that is tailored to perform well on instances that are mostly bi-directed. For such instances, we adapt techniques from the well-researched vertex cover problem. Our core idea is an iterative reduction to vertex cover. To this end, we also develop a new reduction rule that reduces the number of not bi-directed edges. With the resulting algorithm, we were able to win third place in the exact track of the PACE challenge. We perform computational experiments and compare the running time to other exact algorithms, in particular to the winning algorithm in PACE. Our experiments show that we outpace the other algorithms on instances that have a low density of uni-directed edges.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • directed feedback vertex set
  • vertex cover
  • reduction rules


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