Meta-theorems for Parameterized Streaming Algorithms

The streaming model was introduced to parameterized complexity independently by Fafianie and Kratsch[MFCS14] and by Chitnis, Cormode, Hajiaghayi and Monemizadeh [SODA15]. Subsequently, it was broadened by Chitnis, Cormode, Esfandiari, Hajiaghayi and Monemizadeh [SPAA15] and by Chitnis, Cormode, Esfandiari, Hajiaghayi, McGregor, Monemizadeh and Vorotnikova [SODA16]. Despite its strong motivation, the applicability of the streaming model to central problems in parameterized complexity has remained, for almost a decade, quite limited. Indeed, due to simple Ω(n)-space lower bounds for many of these problems, the k⁰⁽¹⁾·polylog(n)-spacerequirement in the model is too strict.

Thus, we explore semi-streaming algorithms for parameterized graph problems, and present the first systematic study of this topic. Crucially, we aim to construct succinct representations of the input on which optimal post-processing time complexity can be achieved.

•We devise meta-theorems specifically designed for parameterized streaming and demonstrate their applicability by obtaining the first k⁰⁽¹⁾·n·polylog(n)-space streaming algorithms for well-studied problems such as Feedback Vertex Set on Tournaments,Cluster Vertex Deletion,Proper Interval Vertex DeletionandBlock Vertex Deletion. In the process, we demonstrate a fundamental connection between semi-streaming algorithms for recognizing graphs in a graph class H and semi-streaming algorithms for the problem of vertex deletion intoH.

•We present an algorithmic machinery for obtaining streaming algorithms for cut problems and exemplify this by giving the first k⁰⁽¹⁾·n·polylog(n)-space streaming algorithms for Graph Bipartitization, Multiway Cut and Subset Feedback Vertex Set