等待时间约束下时间分离器的求解复杂性
The Complexity of Finding Temporal Separators under Waiting Time Constraints
摘要：
在这项工作中，我们调查的计算复杂性不安分的时间$(s,z)$ -分离，我们被问到是否有可能破坏所有不安分的时间路径之间的两个不同的顶点$s$和$z$删除最多$k$顶点从时间图。时间图有一个固定的顶点，但边缘有（离散）时间戳。不稳定的时间路径使用具有非递减时间戳的边，并且在每个顶点处花费的时间不得超过给定的持续时间$Δ$。不稳定时态$(s,z)$ -分离自然地推广了NP难时态$(s,z)$ -分离问题。我们表明，不安的时间$(s,z)$ -分离是完整的$Σ_2^\text{P}$，位于第二层的多项式时间层次的复杂性类。我们进一步提供了一些见解的参数化的复杂性不安的时间$(s,z)$ -分离参数化的分隔符大小$k$。
英文摘要：
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 $Σ_2^\text{P}$, 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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