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We investigate the gap between theory and practice for exact branching algorithms. In theory, branch-and-reduce algorithms currently have the best time complexity for numerous important problems. On the other hand, in practice,…
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…
We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a positive cost function c: V-> Z^{+}, a partition $P_1,..., P_r$ of the edge set $E$, and a parameter $k_i$ for each…
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…
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
In this paper, we study two generalizations of Vertex Cover and Edge Cover, namely Colorful Vertex Cover and Colorful Edge Cover. In the Colorful Vertex Cover problem, given an $n$-vertex edge-colored graph $G$ with colors from $\{1,…
This work introduces two techniques for the design and analysis of branching algorithms, illustrated through the case study of the Vertex Cover problem. First, we present a method for automatically generating branching rules through a…
In this paper we tackle the problem of persistently covering a complex non-convex environment with a team of robots. We consider scenarios where the coverage quality of the environment deteriorates with time, requiring to constantly revisit…
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…
The paper presents an algorithm for minimum vertex cover problem, which is an NP-Complete problem. The algorithm computes a minimum vertex cover of each input simple graph. Tested by the attached MATLAB programs, Stage 1 of the algorithm is…
We consider a natural variant of the Erd\H{o}s-R\'enyi random graph process in which $k$ vertices are special and are never put into the same connected component. The model is natural and interesting on its own, but is actually inspired by…
A common approach for designing scalable algorithms for massive data sets is to distribute the computation across, say $k$, machines and process the data using limited communication between them. A particularly appealing framework here is…
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 $R_1 \setminus R_2$…
Optimization problems consist of either maximizing or minimizing an objective function. Instead of looking for a maximum solution (resp. minimum solution), one can find a minimum maximal solution (resp. maximum minimal solution). Such…
In this paper we show that the problem of identifying an edge $(i,j)$ in a graph $G$ such that there exists an optimal vertex cover $S$ of $G$ containing exactly one of the nodes $i$ and $j$ is NP-hard. Such an edge is called a weak edge.…
Temporal graphs naturally model graphs whose underlying topology changes over time. Recently, the problems TEMPORAL VERTEX COVER (or TVC) and SLIDING-WINDOW TEMPORAL VERTEX COVER(or $\Delta$-TVC for time-windows of a fixed-length $\Delta$)…
Capacitated Vertex Cover is the hard-capacitated variant of Vertex Cover: given a graph, a capacity for every vertex, and an integer $k$, the task is to select at most $k$ vertices that cover all edges and assign each edge to one of its…
Most optimization problems are notoriously hard. Considerable efforts must be spent in obtaining an optimal solution to certain instances that we encounter in the real world scenarios. Often it turns out that input instances get modified…
Eternal vertex cover problem is a variant of the classical vertex cover problem modeled as a two player attacker-defender game. Computing eternal vertex cover number of graphs is known to be NP-hard in general and the complexity status of…
Modern, inherently dynamic systems are usually characterized by a network structure, i.e. an underlying graph topology, which is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph can be represented…