TY - GEN

T1 - On Finding Separators in Temporal Split and Permutation Graphs

AU - Maack, Nicolas

AU - Molter, Hendrik

AU - Niedermeier, Rolf

AU - Renken, Malte

N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

PY - 2021/1/1

Y1 - 2021/1/1

N2 - Disconnecting two vertices s and z in a graph by removing a minimum number of vertices is a fundamental problem in algorithmic graph theory. This (s, z)-Separation problem is well-known to be polynomial solvable and serves as an important primitive in many applications related to network connectivity. We study the NP-hard Temporal (s, z) -Separation problem on temporal graphs, which are graphs with fixed vertex sets but edge sets that change over discrete time steps. We tackle this problem by restricting the layers (i.e., graphs characterized by edges that are present at a certain point in time) to specific graph classes. We restrict the layers of the temporal graphs to be either all split graphs or all permutation graphs (both being perfect graph classes) and provide both intractability and tractability results. In particular, we show that in general Temporal (s, z) -Separation remains NP-hard both on temporal split and temporal permutation graphs, but we also spot promising islands of fixed-parameter tractability particularly based on parameterizations that measure the amount of “change over time”.

AB - Disconnecting two vertices s and z in a graph by removing a minimum number of vertices is a fundamental problem in algorithmic graph theory. This (s, z)-Separation problem is well-known to be polynomial solvable and serves as an important primitive in many applications related to network connectivity. We study the NP-hard Temporal (s, z) -Separation problem on temporal graphs, which are graphs with fixed vertex sets but edge sets that change over discrete time steps. We tackle this problem by restricting the layers (i.e., graphs characterized by edges that are present at a certain point in time) to specific graph classes. We restrict the layers of the temporal graphs to be either all split graphs or all permutation graphs (both being perfect graph classes) and provide both intractability and tractability results. In particular, we show that in general Temporal (s, z) -Separation remains NP-hard both on temporal split and temporal permutation graphs, but we also spot promising islands of fixed-parameter tractability particularly based on parameterizations that measure the amount of “change over time”.

KW - Connectivity problems

KW - Fixed-parameter tractability

KW - NP-hardness

KW - Special graph classes

KW - Temporal graphs

UR - http://www.scopus.com/inward/record.url?scp=85115447557&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-86593-1_27

DO - 10.1007/978-3-030-86593-1_27

M3 - Conference contribution

AN - SCOPUS:85115447557

SN - 9783030865924

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 385

EP - 398

BT - Fundamentals of Computation Theory - 23rd International Symposium, FCT 2021, Proceedings

A2 - Bampis, Evripidis

A2 - Pagourtzis, Aris

PB - Springer Science and Business Media Deutschland GmbH

T2 - 23rd International Symposium on Fundamentals of Computation Theory, FCT 2021

Y2 - 12 September 2021 through 15 September 2021

ER -