Streaming is a model where an input graph is provided one edge at a time, instead of being able to inspect it at will. In this work, we take a parameterized approach by assuming a vertex cover of the graph is given, building on work of Bishnu et al. [COCOON 2020]. We show the further potency of combining this parameter with the Adjacency List streaming model to obtain results for vertex deletion problems. This includes kernels, parameterized algorithms, and lower bounds for the problems of Pi-free Deletion, H-free Deletion, and the more specific forms of Cluster Vertex Deletion and Odd Cycle Transversal. We focus on the complexity in terms of the number of passes over the input stream, and the memory used. This leads to a pass/memory trade-off, where a different algorithm might be favourable depending on the context and instance. We also discuss implications for parameterized complexity in the non-streaming setting.

翻译：流化是一种模型, 输入图一次提供一个边缘, 而不是可以随意检查它。 在这项工作中, 我们以Bishnu 等人的工作为基础, [COON 2020], 假设图形的顶层覆盖为参数参数。 我们展示了将这个参数与相邻列表流模式相结合以获得顶部删除问题结果的进一步能力。 这包括内核、 参数化算法、 以及无 Pi- deletion 、 H- free Deletion 和 Group Vertex deletion 和 Od Cird Curd Courd Transversal 问题的较低界限。 我们关注输入流的通过次数和使用记忆的复杂程度。 这导致一个通过/ 模拟交易模式, 不同的算法可能因上下文和实例而有利。 我们还讨论了非流式设置中参数化复杂程度的影响 。