Related papers: Fully Dynamic Geometric Vertex Cover and Matching
Finding a minimum vertex cover in a network is a fundamental NP-complete graph problem. One way to deal with its computational hardness, is to trade the qualitative performance of an algorithm (allowing non-optimal outputs) for an improved…
Edge-Geodetic Sets play a crucial role in network monitoring and optimization, wherein the goal is to strategically place monitoring stations on vertices of a network, represented as a graph, to ensure complete coverage of edges and…
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…
We study the minimum vertex cover problem in the following stochastic setting. Let $G$ be an arbitrary given graph, $p \in (0, 1]$ a parameter of the problem, and let $G_p$ be a random subgraph that includes each edge of $G$ independently…
Finding the maximum matching in bipartite graphs is a fundamental graph operation widely used in various fields. To expedite the acquisition of the maximum matching, Karp and Sipser introduced two data reduction rules aimed at decreasing…
We study fundamental graph problems such as graph connectivity, minimum spanning forest (MSF), and approximate maximum (weight) matching in a distributed setting. In particular, we focus on the Adaptive Massively Parallel Computation (AMPC)…
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…
We present a work optimal algorithm for parallel fully batch-dynamic maximal matching against an oblivious adversary. It processes batches of updates (either insertions or deletions of edges) in constant expected amortized work per edge…
To solve the combinatorial optimization problems especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of…
We propose and study the graph-theoretical problem EXISTS-PMVC: the existence of perfect matching under vertex-color constraints on graphs with bi-colored edges. EXISTS-PMVC is of special interest because of its motivation from…
Given a set of $n$ points in the plane, the Unit Disk Cover (UDC) problem asks to compute the minimum number of unit disks required to cover the points, along with a placement of the disks. The problem is NP-hard and several approximation…
Many algorithms which exactly solve hard problems require branching on more or less complex structures in order to do their job. Those who design such algorithms often find themselves doing a meticulous analysis of numerous different cases…
A geometric intersection graph is constructed over a set of geometric objects, where each vertex represents a distinct object and an edge connects two vertices if and only if the corresponding objects intersect. We examine the problem of…
In the Maximum Minimal Vertex Cover (MMVC) problem, we are given a graph $G$ and a positive integer $k$, and the objective is to decide whether $G$ contains a minimal vertex cover of size at least $k$. Motivated by the kernelization of MMVC…
In the Minimum Consistent Subset (MCS) problem, we are presented with a connected simple undirected graph $G=(V,E)$, consisting of a vertex set $V$ of size $n$ and an edge set $E$. Each vertex in $V$ is assigned a color from the set…
Most graphs in real life keep changing with time. These changes can be in the form of insertion or deletion of edges or vertices. Such rapidly changing graphs motivate us to study dynamic graph algorithms. However, three important graph…
The phylogenetic tree construction is to infer the evolutionary relationship between species from the experimental data. However, the experimental data are often imperfect and conflicting each others. Therefore, it is important to extract…
We study the fully dynamic maximum matching problem. In this problem, the goal is to efficiently maintain an approximate maximum matching of a graph that is subject to edge insertions and deletions. Our focus is on algorithms that maintain…
In the context of the chromatic-number problem, a critical graph is an instance where the deletion of any element would decrease the graph's chromatic number. Such instances have shown to be interesting objects of study for deepen the…
We investigate dynamic versions of geometric set cover and hitting set where points and ranges may be inserted or deleted, and we want to efficiently maintain an (approximately) optimal solution for the current problem instance. While their…