Log In Sign Up

The Complexity of Finding Temporal Separators under Waiting Time Constraints

by   Hendrik Molter, et al.

In this work, we investigate the computational complexity of Restless Temporal (s,z)-Separation, where we are asked whether it is possible to destroy all restless temporal paths between two distinct vertices s and z by deleting at most k vertices from a temporal graph. A temporal graph has a fixed vertex but the edges have (discrete) time stamps. A restless temporal path uses edges with non-decreasing time stamps and the time spent at each vertex must not exceed a given duration Δ. Restless Temporal (s,z)-Separation naturally generalizes the NP-hard Temporal (s,z)-Separation problem. We show that Restless Temporal (s,z)-Separation is complete for Σ_2^P, a complexity class located in the second level of the polynomial time hierarchy. We further provide some insights in the parameterized complexity of Restless Temporal (s,z)-Separation parameterized by the separator size k.


page 1

page 2

page 3

page 4


The Computational Complexity of Finding Temporal Paths under Waiting Time Constraints

Computing a (shortest) path between two vertices in a graph is one of th...

Temporal Graph Classes: A View Through Temporal Separators

We investigate the computational complexity of separating two distinct v...

On Finding Separators in Temporal Split and Permutation Graphs

Removing all connections between two vertices s and z in a graph by remo...

The Computational Complexity of Finding Separators in Temporal Graphs

Vertex separators, that is, vertex sets whose deletion disconnects two d...

Mengerian graphs: characterization and recognition

A temporal graph G is a graph that changes with time. More specifically,...

Deleting edges to restrict the size of an epidemic in temporal networks

A variety of potentially disease-spreading contact networks can be natur...

Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible

We analyze the computational complexity of the many types of pencil-and-...