TY - GEN
T1 - Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover
AU - Angrick, Sebastian
AU - Bals, Ben
AU - Casel, Katrin
AU - Cohen, Sarel
AU - Friedrich, Tobias
AU - Hastrich, Niko
AU - Hradilak, Theresa
AU - Issac, Davis
AU - Kißig, Otto
AU - Schmidt, Jonas
AU - Wendt, Leo
N1 - Publisher Copyright:
© 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.
PY - 2023/7
Y1 - 2023/7
N2 - 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.
AB - 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.
KW - directed feedback vertex set
KW - reduction rules
KW - vertex cover
UR - http://www.scopus.com/inward/record.url?scp=85168674648&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.SEA.2023.10
DO - 10.4230/LIPIcs.SEA.2023.10
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AN - SCOPUS:85168674648
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 21st International Symposium on Experimental Algorithms, SEA 2023
A2 - Georgiadis, Loukas
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 21st International Symposium on Experimental Algorithms, SEA 2023
Y2 - 24 July 2023 through 26 July 2023
ER -