Related papers: Dynamic Set Cover: Improved Algorithms & Lower Bou…

We consider the classic Set Cover problem in the data stream model. For $n$ elements and $m$ sets ($m\geq n$) we give a $O(1/\delta)$-pass algorithm with a strongly sub-linear $\tilde{O}(mn^{\delta})$ space and logarithmic approximation…

We present a new distance oracle in the fully dynamic setting: given a weighted undirected graph $G=(V,E)$ with $n$ vertices undergoing both edge insertions and deletions, and an arbitrary parameter $\epsilon$ where $\epsilon\in[1/\log^{c}…

Maintaining maximal independent set in dynamic graph is a fundamental open problem in graph theory and the first sublinear time deterministic algorithm was came up by Assadi, Onak, Schieber and Solomon(STOC'18), which achieves $O(m^{3/4})$…

We consider the PageRank problem in the dynamic setting, where the goal is to explicitly maintain an approximate PageRank vector $\pi \in \mathbb{R}^n$ for a graph under a sequence of edge insertions and deletions. Our main result is a…

The maximum matching problem in dynamic graphs subject to edge updates (insertions and deletions) has received much attention over the last few years; a multitude of approximation/time tradeoffs were obtained, improving upon the folklore…

We show that Set Cover on instances with $N$ elements cannot be approximated within $(1-\gamma)\ln N$-factor in time exp($N^{\gamma-\delta})$, for any $0 < \gamma < 1$ and any $\delta > 0$, assuming the Exponential Time Hypothesis. This…

We revisit classic string problems considered in the area of parameterized complexity, and study them through the lens of dynamic data structures. That is, instead of asking for a static algorithm that solves the given instance efficiently,…

We study fully dynamic algorithms for maximum matching. This is a well-studied problem, known to admit several update-time/approximation trade-offs. For instance, it is known how to maintain a 1/2-approximate matching in $\log^{O(1)} n$…

Despite significant research efforts, the state-of-the-art algorithm for maintaining an approximate matching in fully dynamic graphs has a polynomial {worst-case} update time, even for very poor approximation guarantees. In a recent…

We consider the problem of maintaining an approximate maximum independent set of geometric objects under insertions and deletions. We present data structures that maintain a constant-factor approximate maximum independent set for broad…

The SetCover problem has been extensively studied in many different models of computation, including parallel and distributed settings. From an approximation point of view, there are two standard guarantees: an $O(\log…

We present dynamic algorithms with polylogarithmic update time for estimating the size of the maximum matching of a graph undergoing edge insertions and deletions with approximation ratio strictly better than $2$. Specifically, we obtain a…

In the dynamic set cover problem, the input is a dynamic universe of elements and a fixed collection of sets. As elements are inserted or deleted, the goal is to efficiently maintain an approximate minimum set cover. While the past decade…

We study dynamic $(1-\epsilon)$-approximate rounding of fractional matchings -- a key ingredient in numerous breakthroughs in the dynamic graph algorithms literature. Our first contribution is a surprisingly simple deterministic rounding…

We study maximum matchings in fully dynamic graphs, which are graphs that undergo both edge insertions and deletions. Our focus is on algorithms that estimate the size of maximum matching after each update while spending a small time. An…

The classic technique of Baker [J. ACM '94] is the most fundamental approach for designing approximation schemes on planar, or more generally topologically-constrained graphs, and it has been applied in a myriad of different variants and…

In this paper, we consider dynamic matroids, where elements can be inserted to or deleted from the ground set over time. The independent sets change to reflect the current ground set. As matroids are central to the study of many…

We present a dynamic algorithm for maintaining $(1+\epsilon)$-approximate maximum eigenvector and eigenvalue of a positive semi-definite matrix $A$ undergoing \emph{decreasing} updates, i.e., updates which may only decrease eigenvalues.…

We improve the running times of $O(1)$-approximation algorithms for the set cover problem in geometric settings, specifically, covering points by disks in the plane, or covering points by halfspaces in three dimensions. In the unweighted…

Several algorithms with an approximation guarantee of $O(\log n)$ are known for the Set Cover problem, where $n$ is the number of elements. We study a generalization of the Set Cover problem, called the Partition Set Cover problem. Here,…