Thesis for the degree Master of Science

We study the well known vertex cover problem in various data streaming settings. Our first result considers a special family of graphs, the Vertex-Disjoint Paths (V DP ) family. We say that a graph G is in the V DP family if the edges of G are a union of vertex disjoint paths. For a V DP graph with n vertices given in a dynamic stream, in which both insertions and deletions are allowed, we provide a randomized algorithm for estimating the size of an optimal vertex cover within ( 4 + ε) factor, using Õ(ε −1n) bits of space. Our space bound is near-optimal because a result by Esfandiari et al. [EHL+15] implies that even when the input is limited to graphs in the V DP family, a weaker (32−ε)-estimation algorithm already requires Ω( √ n) space, for every constant ε > 0. We continue by exploring general graphs in two other streaming models and develop algorithms for vertex cover approximation in these models. For the dynamic multi-pass model, in which both insertions and deletions are permitted and few passes over the stream are allowed, we provide a randomized p-pass algorithm that uses Õ(n1+1/p) space and returns a feasible vertex cover at most twice the size of an optimal one. For the sliding window model, in which our interest is only in the last w elements in the stream, we provide a deterministic algorithm that uses O(1εn lg n) bits of space and returns a vertex cover at most (8 + ε) times the size of an optimal one.