Related papers: Fully Dynamic Set Cover via Hypergraph Maximal Mat…
The \emph{$\ell_2$ tracking problem} is the task of obtaining a streaming algorithm that, given access to a stream of items $a_1,a_2,a_3,\ldots$ from a universe $[n]$, outputs at each time $t$ an estimate to the $\ell_2$ norm of the…
This paper presents a comprehensive study of algorithms for maintaining the number of all connected four-vertex subgraphs in a dynamic graph. Specifically, our algorithms maintain the number of paths of length three in deterministic…
An $\alpha$-spanner of a graph $ G $ is a subgraph $ H $ such that $ H $ preserves all distances of $ G $ within a factor of $ \alpha $. In this paper, we give fully dynamic algorithms for maintaining a spanner $ H $ of a graph $ G $…
Reachability, distance, and matching are some of the most fundamental graph problems that have been of particular interest in dynamic complexity theory in recent years [DKMSZ18, DMVZ18, DKMTVZ20]. Reachability can be maintained with…
We consider the problem of maintaining a maximal independent set (MIS) in a dynamic graph subject to edge insertions and deletions. Recently, Assadi, Onak, Schieber and Solomon (STOC 2018) showed that an MIS can be maintained in sublinear…
We give the first non-trivial fully dynamic probabilistic tree embedding algorithm for weighted graphs undergoing edge insertions and deletions. We obtain a trade-off between amortized update time and expected stretch against an oblivious…
We study approximation algorithms for several variants of the MaxCover problem, with the focus on algorithms that run in FPT time. In the MaxCover problem we are given a set N of elements, a family S of subsets of N, and an integer K. The…
We consider the well-studied problem of finding a perfect matching in $d$-regular bipartite graphs with $2n$ vertices and $m = nd$ edges. While the best-known algorithm for general bipartite graphs (due to Hopcroft and Karp) takes $O(m…
We study the approximability of instances of the minimum entropy set cover problem, parameterized by the average frequency of a random element in the covering sets. We analyze an algorithm combining a greedy approach with another one biased…
In submodular covering problems, we are given a monotone, nonnegative submodular function $f: 2^N \rightarrow\mathbb{R}_+$ and wish to find the min-cost set $S\subseteq N$ such that $f(S)=f(N)$. This captures SetCover when $f$ is a coverage…
Single Source Shortest Paths ($\textrm{SSSP}$) is among the most well-studied problems in computer science. In the incremental (resp. decremental) setting, the goal is to maintain distances from a fixed source in a graph undergoing edge…
We study the problem of exact completion for $m \times n$ sized matrix of rank $r$ with the adaptive sampling method. We introduce a relation of the exact completion problem with the sparsest vector of column and row spaces (which we call…
We present two algorithms for dynamically maintaining a spanning forest of a graph undergoing edge insertions and deletions. Our algorithms guarantee {\em worst-case update time} and work against an adaptive adversary, meaning that an edge…
The graph matching problem seeks to find an alignment between the nodes of two graphs that minimizes the number of adjacency disagreements. Solving the graph matching is increasingly important due to it's applications in operations…
Research involving computing with mobile agents is a fast-growing field, given the advancement of technology in automated systems, e.g., robots, drones, self-driving cars, etc. Therefore, it is pressing to focus on solving classical network…
In this paper we further investigate the well-studied problem of finding a perfect matching in a regular bipartite graph. The first non-trivial algorithm, with running time $O(mn)$, dates back to K\"{o}nig's work in 1916 (here $m=nd$ is the…
We study the classic set cover problem in the streaming model: the sets that comprise the instance are revealed one by one in a stream and the goal is to solve the problem by making one or few passes over the stream while maintaining a…
Consider the classical Min-Sum Set Cover problem: We are given a universe $\mathcal{U}$ of $n$ elements and a collection $\mathcal{S}$ of $k$ subsets of $\mathcal{U}$. Moreover, a cost function is associated with each set. The goal is to…
Data-analysis tasks often involve an iterative process, which requires refining previous solutions. For instance, when analyzing dynamic social networks, we may be interested in monitoring the evolution of a community that was identified at…
A tree-packing is a collection of spanning trees of a graph. It has been a useful tool for computing the minimum cut in static, dynamic, and distributed settings. In particular, [Thorup, Comb. 2007] used them to obtain his dynamic min-cut…