Fixed Parameter Tractability of Graph Deletion Problems over Data Streams

Abstract

The study of parameterized streaming complexity on graph problems was initiated by Fafianie et al. (MFCS’14) and Chitnis et al. (SODA’15 and SODA’16). In this work, we initiate a systematic study of parameterized streaming complexity of graph deletion problems – \(\mathcal {F}\) -Subgraph deletion, \(\mathcal {F}\) -Minor deletion in the four most well-studied streaming models: the \(\textsc {Ea}\) (edge arrival), \(\textsc {Dea}\) (dynamic edge arrival), \(\textsc {Va}\) (vertex arrival) and Al (adjacency list) models. Our main conceptual contribution is to overcome the obstacles to efficient parameterized streaming algorithms by utilizing the power of parameterization. We focus on the vertex cover size K as the parameter for the parameterized graph deletion problems we consider. At the same time, most of the previous work in parameterized streaming complexity was restricted to the Ea (edge arrival) or Dea (dynamic edge arrival) models. In this work, we consider the four most well-studied streaming models: the Ea, Dea, Va (vertex arrival) and Al (adjacency list) models.