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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…
Modern networks are highly dynamic, and temporal graphs capture these changes through discrete edge appearances on a fixed vertex set, known in advance up to the graph's lifetime. The Vertex Cover problem extends to the temporal setting as…
Algorithms for finding minimum or bounded vertex covers in graphs use a branch-and-reduce strategy, which involves exploring a highly imbalanced search tree. Prior GPU solutions assign different thread blocks to different sub-trees, while…
We consider the Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families $\calR$ where $R_1 \setminus R_2$…
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…
A cactus is a connected graph that does not contain $K_4 - e$ as a minor. Given a graph $G = (V, E)$ and integer $k \ge 0$, Cactus Vertex Deletion (also known as Diamond Hitting Set) is the problem of deciding whether $G$ has a vertex set…
Counting the solution number of combinational optimization problems is an important topic in the study of computational complexity, especially on the #P-complete complexity class. In this paper, we first investigate some organizations of…
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…
For a collection $\mathcal{F}$ of graphs, the $\mathcal{F}$-\textsc{Contraction} problem takes a graph $G$ and an integer $k$ as input and decides if $G$ can be modified to some graph in $\mathcal{F}$ using at most $k$ edge contractions.…
A linear-time algorithm for generating auxiliary subgraphs for the 3-edge-connected components of a connected multigraph is presented. The algorithm uses an innovative graph contraction operation and makes only one pass over the graph. By…
Covering problems are classical computational problems concerning whether a certain combinatorial structure 'covers' another. For example, the minimum vertex covering problem aims to find the smallest set of vertices in a graph so that each…
The weighted $k$-center problem in graphs is a classical facility location problem where we place $k$ centers on the graph, which minimize the maximum weighted distance of a vertex to its nearest center. We study this problem when the…
In this paper, we perform theoretical analyses on the behaviour of an evolutionary algorithm and a randomised search algorithm for the dynamic vertex cover problem based on its dual formulation. The dynamic vertex cover problem has already…
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. Using binary indexed tree data structure, we improve algorithms for calculating the size and the number of…
Consider a graph with a rotation system, namely, for every vertex, a circular ordering of the incident edges. Given such a graph, an angle cover maps every vertex to a pair of consecutive edges in the ordering -- an angle -- such that each…
Finding small vertex covers in a graph has applications in numerous domains. Two common formulations of the problem include: Minimum Vertex Cover, which finds the smallest vertex cover in a graph, and Parameterized Vertex Cover, which finds…
Some rigorous results and statistics of the solution space of Vertex-Covers on bipartite graphs are given in this paper. Based on the $K\ddot{o}nig$'s theorem, an exact solution space expression algorithm is proposed and statistical…
We study two related problems on simple, un-directed graphs: Edge Deletion to Cactus and Spanning Tree to Cactus. Edge Deletion to Cactus has been known to be NP-hard on general graphs at least since 1988. We show improved exact algorithms…
This article studies the Minimum Spanning Tree Problem under Explorable Uncertainty as well as a related vertex uncertainty version of the problem. We particularly consider special instance types, including cactus graphs, for which we…
In the solution discovery problem for a search problem on graphs, we are given an initial placement of $k$ tokens on the vertices of a graph and asked whether this placement can be transformed into a feasible solution by applying a small…