Related papers: Semi-Streaming Set Cover
A rounding scheme for set cover has served as an important component in design of approximation algorithms for the problem, and there exists an H_s-approximate rounding scheme, where s denotes the maximum subset size, directly implying an…
Let $\mathcal{H}=(V,\mathcal{E})$ be a hypergraph with maximum edge size $\ell$ and maximum degree $\Delta$. For given numbers $b_v\in \mathbb{N}_{\geq 2}$, $v\in V$, a set multicover in $\mathcal{H}$ is a set of edges $C \subseteq…
Coverage problems are central in optimization and have a wide range of applications in data mining and machine learning. While several distributed algorithms have been developed for coverage problems, the existing methods suffer from…
In the Connected Dominating Set problem we are given a graph $G=(V,E)$ and seek a minimum size dominating set $S \subseteq V$ such that the subgraph $G[S]$ of $G$ induced by $S$ is connected. In the $2$-Edge-Connected Dominating Set problem…
We consider the problem of maximizing a non-negative submodular function under the $b$-matching constraint, in the semi-streaming model. When the function is linear, monotone, and non-monotone, we obtain the approximation ratios of…
This study considers the (soft) capacitated vertex cover problem in a dynamic setting. This problem generalizes the dynamic model of the vertex cover problem, which has been intensively studied in recent years. Given a dynamically changing…
We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
Constructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by…
In recent years, there has been a growing interest in solving various graph coloring problems in the streaming model. The initial algorithms in this line of work are all crucially randomized, raising natural questions about how important a…
Low-rank approximation in data streams is a fundamental and significant task in computing science, machine learning and statistics. Multiple streaming algorithms have emerged over years and most of them are inspired by randomized…
The following question arises naturally in the study of graph streaming algorithms: "Is there any graph problem which is "not too hard", in that it can be solved efficiently with total communication (nearly) linear in the number $n$ of…
In this thesis, we explore streaming algorithms for approximating constraint satisfaction problems (CSPs). The setup is roughly the following: A computer has limited memory space, sees a long "stream" of local constraints on a set of…
The widely studied edge modification problems ask how to minimally alter a graph to satisfy certain structural properties. In this paper, we introduce and study a new edge modification problem centered around transforming a given graph into…
Any graph with maximum degree $\Delta$ admits a proper vertex coloring with $\Delta + 1$ colors that can be found via a simple sequential greedy algorithm in linear time and space. But can one find such a coloring via a sublinear algorithm?…
We study the $k$-connectivity augmentation problem ($k$-CAP) in the single-pass streaming model. Given a $(k-1)$-edge connected graph $G=(V,E)$ that is stored in memory, and a stream of weighted edges $L$ with weights in $\{0,1,\dots,W\}$,…
In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…
Partitioning an input graph over a set of workers is a complex operation. Objectives are twofold: split the work evenly, so that every worker gets an equal share, and minimize edge cut to achieve a good work locality (i.e. workers can work…
In this paper, we introduce the problem of Matroid-Constrained Vertex Cover: given a graph with weights on the edges and a matroid imposed on the vertices, our problem is to choose a subset of vertices that is independent in the matroid,…
Given a convex polygon $P$ with $n$ vertices, the two-center problem is to find two congruent closed disks of minimum radius such that they completely cover $P$. We propose an algorithm for this problem in the streaming setup, where the…