Streaming Deletion Problems Parameterized by Vertex Cover

TL;DR

This paper explores streaming algorithms for vertex deletion problems in graphs, leveraging a given vertex cover to develop kernels, algorithms, and bounds, with a focus on pass and memory trade-offs.

Contribution

It introduces a parameterized streaming approach using vertex cover, extending prior work to obtain new algorithms, kernels, and lower bounds for deletion problems.

Findings

Developed streaming kernels and algorithms for Pi-free and H-free Deletion

Established pass/memory trade-offs for vertex deletion problems

Discussed implications for parameterized complexity in non-streaming settings

Abstract

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.