Related papers: Approximation Algorithm for Minimum Weight $(k,m)$…
We consider the maximum vertex-weighted matching problem (MVM), in which non-negative weights are assigned to the vertices of a graph, the weight of a matching is the sum of the weights of the matched vertices, and we are required to…
We study the densest subgraph problem and its NP-hard densest at-most-$k$ subgraph variant through the lens of learning-augmented algorithms. We show that, given a reasonably accurate predictor that estimates whether a node belongs to the…
The minimum-weight $2$-edge-connected spanning subgraph (2-ECSS) problem is a natural generalization of the well-studied minimum-weight spanning tree (MST) problem, and it has received considerable attention in the area of network design.…
The Minimum Dominating Set (MDS) problem is not only one of the most fundamental problems in distributed computing, it is also one of the most challenging ones. While it is well-known that minimum dominating sets cannot be approximated…
For a graph $G$ and a non-negative integral weight function $w$ on the vertex set of $G$, a set $S$ of vertices of $G$ is $w$-safe if $w(C)\geq w(D)$ for every component $C$ of the subgraph of $G$ induced by $S$ and every component $D$ 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…
In the Priority Steiner Tree (PST) problem, we are given an undirected graph $G=(V,E)$ with a source $s \in V$ and terminals $T \subseteq V \setminus \{s\}$, where each terminal $v \in T$ requires a nonnegative priority $P(v)$. The goal is…
Network applications, such as multimedia streaming and video conferencing, impose growing requirements over Quality of Service (QoS), including bandwidth, delay, jitter, etc. Meanwhile, networks are expected to be load-balanced,…
The problem of space-efficient depth-first search (DFS) is reconsidered. A particularly simple and fast algorithm is presented that, on a directed or undirected input graph $G=(V,E)$ with $n$ vertices and $m$ edges, carries out a DFS in…
In the $k$-Center problem, we are given a graph $G=(V,E)$ with positive edge weights and an integer $k$ and the goal is to select $k$ center vertices $C \subseteq V$ such that the maximum distance from any vertex to the closest center…
We give the first almost-linear time algorithm for computing the \emph{maximal $k$-edge-connected subgraphs} of an undirected unweighted graph for any constant $k$. More specifically, given an $n$-vertex $m$-edge graph $G=(V,E)$ and a…
For a set of $n$ points in the plane, this paper presents simple kinetic data structures (KDS's) for solutions to some fundamental proximity problems, namely, the all nearest neighbors problem, the closest pair problem, and the Euclidean…
Let $G = (V,E)$ be a simple, undirected and connected graph. A connected dominating set $S \subseteq V$ is a secure connected dominating set of $G$, if for each $ u \in V\setminus S$, there exists $v\in S$ such that $(u,v) \in E$ and the…
Computational complexity and approximation algorithms are reported for a problem of stabbing a set of straight line segments with the least cardinality set of disks of fixed radii $r>0$ where the set of segments forms a straight line…
In Maximum $k$-Vertex Cover (Max $k$-VC), the input is an edge-weighted graph $G$ and an integer $k$, and the goal is to find a subset $S$ of $k$ vertices that maximizes the total weight of edges covered by $S$. Here we say that an edge is…
We present a family of fast pseudo-approximation algorithms for the minimum balanced vertex separator problem in a graph. Given a graph $G=(V,E)$ with $n$ vertices and $m$ edges, and a (constant) balance parameter $c\in(0,1/2)$, where $G$…
The volume of image repositories continues to grow. Despite the availability of content-based addressing, we still lack a lightweight tool that allows us to discover images of distinct characteristics from a large collection. In this paper,…
In this paper, we study the $k$-forest problem in the model of resource augmentation. In the $k$-forest problem, given an edge-weighted graph $G(V,E)$, a parameter $k$, and a set of $m$ demand pairs $\subseteq V \times V$, the objective is…
We study the classic NP-Hard problem of finding the maximum $k$-set coverage in the data stream model: given a set system of $m$ sets that are subsets of a universe $\{1,\ldots,n \}$, find the $k$ sets that cover the most number of distinct…
Densest subgraph discovery (DSD) is a fundamental problem in graph mining. It has been studied for decades, and is widely used in various areas, including network science, biological analysis, and graph databases. Given a graph G, DSD aims…