Parameterized Streaming Algorithms for Vertex Cover
Rajesh Chitnis, Graham Cormode, MohammadTaghi Hajiaghayi, Morteza, Monemizadeh

TL;DR
This paper introduces the first streaming algorithms for the parameterized Vertex Cover problem across various dynamic graph models, combining kernelization and randomized sketches, with proven space complexity bounds.
Contribution
It presents novel parameterized streaming algorithms for Vertex Cover in insertion-only, dynamic, and promised dynamic models, using kernelization and randomized sketches.
Findings
First algorithms for parameterized Vertex Cover in streaming models
Matching lower bounds on space complexity
Effective handling of dynamic graph streams with solutions bounded by parameter k
Abstract
As graphs continue to grow in size, we seek ways to effectively process such data at scale. The model of streaming graph processing, in which a compact summary is maintained as each edge insertion/deletion is observed, is an attractive one. However, few results are known for optimization problems over such dynamic graph streams. In this paper, we introduce a new approach to handling graph streams, by instead seeking solutions for the parameterized versions of these problems where we are given a parameter and the objective is to decide whether there is a solution bounded by . By combining kernelization techniques with randomized sketch structures, we obtain the first streaming algorithms for the parameterized versions of the Vertex Cover problem. We consider the following three models for a graph stream on nodes: 1. The insertion-only model where the edges can only be…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Advanced Graph Theory Research · Optimization and Search Problems
