Related papers: New Approximations for Temporal Vertex Cover on Al…
Temporal graphs are used to abstractly model real-life networks that are inherently dynamic in nature. Given a static underlying graph $G=(V,E)$, a temporal graph on $G$ is a sequence of snapshots $G_t$, one for each time step $t\geq 1$. In…
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 study how we can accelerate the spreading of information in temporal graphs via shifting operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a…
In this work, we follow the current trend on temporal graph realization, where one is given a property P and the goal is to determine whether there is a temporal graph, that is, a graph where the edge set changes over time, with property P…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
The CONTRACTION(vc) problem takes as input a graph $G$ on $n$ vertices and two integers $k$ and $d$, and asks whether one can contract at most $k$ edges to reduce the size of a minimum vertex cover of $G$ by at least $d$. Recently, Lima et…
The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a…
Many real world networks are considered temporal networks, in which the chronological ordering of the edges has importance to the meaning of the data. Performing temporal subgraph matching on such graphs requires the edges in the subgraphs…
We present a general framework of designing efficient dynamic approximate algorithms for optimization on undirected graphs. In particular, we develop a technique that, given any problem that admits a certain notion of vertex sparsifiers,…
We consider temporal graphs with discrete time labels and investigate the size and the approximability of minimum temporally connected spanning subgraphs. We present a family of minimally connected temporal graphs with $n$ vertices and…
Given a graph $G$, let $vc(G)$ and $vc^+(G)$ be the sizes of a minimum and a maximum minimal vertex covers of $G$, respectively. We say that $G$ is well covered if $vc(G)=vc^+(G)$ (that is, all minimal vertex covers have the same size).…
We introduce and study two natural generalizations of the Connected VertexCover (VC) problem: the $p$-Edge-Connected and $p$-Vertex-Connected VC problem (where $p \geq 2$ is a fixed integer). Like Connected VC, both new VC problems are FPT,…
We consider the problem of maintaining a proper $(\Delta + 1)$-vertex coloring in a graph on $n$-vertices and maximum degree $\Delta$ undergoing edge insertions and deletions. We give a randomized algorithm with amortized update time…
Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…
We (nearly) settle the time complexity for computing vertex fault-tolerant (VFT) spanners with optimal sparsity (up to polylogarithmic factors). VFT spanners are sparse subgraphs that preserve distance information, up to a small…
In this paper, we explicitly study the online vertex cover problem, which is a natural generalization of the well-studied ski-rental problem. In the online vertex cover problem, we are required to maintain a monotone vertex cover in a graph…
We consider the directed minimum weight cycle problem in the fully dynamic setting. To the best of our knowledge, so far no fully dynamic algorithms have been designed specifically for the minimum weight cycle problem in general digraphs.…
The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric…
Given a graph $G$ and an integer $k$, the Feedback Vertex Set (FVS) problem asks if there is a vertex set $T$ of size at most $k$ that hits all cycles in the graph. The fixed-parameter tractability status of FVS in directed graphs was a…
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…