Related papers: The generalized vertex cover problem and some vari…
Given a simple undirected graph $G = (V, E)$, the open neighbourhood of a vertex $v \in V$ is defined as $N_G(v) = \{u \in V \mid uv \in E\}$, and the closed neighbourhood as $N_G[v] = N_G(v) \cup \{v\}$. A subset $D \subseteq V$ is called…
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…
The {\sc $c$-Balanced Separator} problem is a graph-partitioning problem in which given a graph $G$, one aims to find a cut of minimum size such that both the sides of the cut have at least $cn$ vertices. In this paper, we present new…
In this paper we present a new semidefinite programming hierarchy for covering problems in compact metric spaces. Over the last years, these kind of hierarchies were developed primarily for geometric packing and for energy minimization…
In a recent paper, Francis, Illickan, Jose and Rajendraprasad showed that every $n$-vertex plane graph $G$ has (under some natural restrictions) a vertex-partition into two sets $V_1$ and $V_2$ such that each $V_i$ is \emph{dominating}…
Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are…
In the Graph Isomorphism problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and transforms G into G'. If yes, then G and G' are said…
Genetic Programming (GP) has found various applications. Understanding this type of algorithm from a theoretical point of view is a challenging task. The first results on the computational complexity of GP have been obtained for problems…
We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…
A {\bf $\mathbf{k}$-majority coloring} of a digraph $D=(V,A)$ is a coloring of $V$ with $k$ colors so that each vertex $v\in V$ has at least as many out-neighbours of color different from its own color as it has out-neighbours with the same…
We show that the problem to decide whether two (convex) polytopes, given by their vertex-facet incidences, are combinatorially isomorphic is graph isomorphism complete, even for simple or simplicial polytopes. On the other hand, we give a…
Dominating set problems are among the most important class of combinatorial problems in graph optimization, from a theoretical as well as from a practical point of view. In this paper, we address the recently introduced (minimum) weighted…
A $k$-coloring of a graph $G=(V,E)$ is called semi-equitable if there exists a partition of its vertex set into independent subsets $V_1,\ldots,V_k$ in such a way that $|V_1| \notin \{\lceil |V|/k\rceil, \lfloor |V|/k \rfloor\}$ and…
We propose an exact algorithm for the Graph Burning Problem ($\texttt{GBP}$), an NP-hard optimization problem that models the spread of influence on social networks. Given a graph $G$ with vertex set $V$, the objective is to find a sequence…
In this paper we present linear time approximation schemes for several generalized matching problems on nonbipartite graphs. Our results include $O_\epsilon(m)$-time algorithms for $(1-\epsilon)$-maximum weight $f$-factor and…
A total coloring of a graph $G = (V, E)$ is an assignment of colors to vertices and edges such that neither two adjacent vertices nor two incident edges get the same color, and, for each edge, the end-points and the edge itself receive…
We investigate preprocessing for vertex-subset problems on graphs. While the notion of kernelization, originating in parameterized complexity theory, is a formalization of provably effective preprocessing aimed at reducing the total…
Subgraph complementation is an operation that toggles all adjacencies inside a selected vertex set. Given a graph \(G\) and a target class \(\mathcal{C}\), the Minimum Subgraph Complementation problem asks for a minimum-size vertex set…
The eternal vertex cover problem is a dynamic variant of the classical vertex cover problem. It is NP-hard to compute the eternal vertex cover number of graphs and known algorithmic results for the problem are very few. This paper presents…
Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…