TY - GEN
T1 - Length-bounded cuts
T2 - 31st International Symposium on Algorithms and Computation, ISAAC 2020
AU - Bentert, Matthias
AU - Heeger, Klaus
AU - Knop, Dušan
N1 - Publisher Copyright:
© Matthias Bentert, Klaus Heeger, and Dušan Knop.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - In the presented paper, we study the Length-Bounded Cut problem for special graph classes as well as from a parameterized-complexity viewpoint. Here, we are given a graph G, two vertices s and t, and positive integers β and λ. The task is to find a set F of edges of size at most β such that every s-t-path of length at most λ in G contains some edge in F. Bazgan et al. [Networks, 2019] conjectured that Length-Bounded Cut admits a polynomial-time algorithm if the input graph G is a proper interval graph. We confirm this conjecture by providing a dynamic-programming based polynomial-time algorithm. Moreover, we strengthen the W[1]-hardness result of Dvořák and Knop [Algorithmica, 2018] for Length-Bounded Cut parameterized by pathwidth. Our reduction is shorter, and the target of the reduction has stronger structural properties. Consequently, we give W[1]-hardness for the combined parameter pathwidth and maximum degree of the input graph. Finally, we prove that Length-Bounded Cut is W[1]-hard for the feedback vertex number. Both our hardness results complement known XP algorithms.
AB - In the presented paper, we study the Length-Bounded Cut problem for special graph classes as well as from a parameterized-complexity viewpoint. Here, we are given a graph G, two vertices s and t, and positive integers β and λ. The task is to find a set F of edges of size at most β such that every s-t-path of length at most λ in G contains some edge in F. Bazgan et al. [Networks, 2019] conjectured that Length-Bounded Cut admits a polynomial-time algorithm if the input graph G is a proper interval graph. We confirm this conjecture by providing a dynamic-programming based polynomial-time algorithm. Moreover, we strengthen the W[1]-hardness result of Dvořák and Knop [Algorithmica, 2018] for Length-Bounded Cut parameterized by pathwidth. Our reduction is shorter, and the target of the reduction has stronger structural properties. Consequently, we give W[1]-hardness for the combined parameter pathwidth and maximum degree of the input graph. Finally, we prove that Length-Bounded Cut is W[1]-hard for the feedback vertex number. Both our hardness results complement known XP algorithms.
KW - Edge-disjoint paths
KW - Feedback vertex number
KW - Pathwidth
UR - http://www.scopus.com/inward/record.url?scp=85100940712&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ISAAC.2020.36
DO - 10.4230/LIPIcs.ISAAC.2020.36
M3 - Conference contribution
AN - SCOPUS:85100940712
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 361
EP - 3614
BT - 31st International Symposium on Algorithms and Computation, ISAAC 2020
A2 - Cao, Yixin
A2 - Cheng, Siu-Wing
A2 - Li, Minming
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Y2 - 14 December 2020 through 18 December 2020
ER -