The Complexity of Finding Temporal Separators under Waiting Time Constraints

Hendrik Molter

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arXiv · 2107.01609

The Complexity of Finding Temporal Separators under Waiting Time Constraints

Hendrik Molter

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Abstract

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 $\Delta$. 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 $\Sigma_2^\text{P}$, 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 $k$.

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Hendrik Molter. 2021-07-04. The Complexity of Finding Temporal Separators under Waiting Time Constraints. https://arxiv.org/abs/2107.01609

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