Related papers: Concurrency Constrained Scheduling with Tree-Like …
We study the scheduling problem of makespan minimization while taking machine conflicts into account. Machine conflicts arise in various settings, e.g., shared resources for pre- and post-processing of tasks or spatial restrictions. In this…
Path cover is a well-known intractable problem that finds a minimum number of vertex disjoint paths in a given graph to cover all the vertices. We show that a variant, where the objective function is not the number of paths but the number…
We introduce a variant of the graph coloring problem, which we denote as {\sc Budgeted Coloring Problem} (\bcp). Given a graph $G$, an integer $c$ and an ordered list of integers $\{b_1, b_2, \ldots, b_c\}$, \bcp asks whether there exists a…
Structural graph parameters, such as treewidth, pathwidth, and clique-width, are a central topic of study in parameterized complexity. A main aim of research in this area is to understand the "price of generality" of these widths: as we…
Color-constrained subgraph problems are those where we are given an edge-colored (directed or undirected) graph and the task is to find a specific type of subgraph, like a spanning tree, an arborescence, a single-source shortest path tree,…
This article is devoted to propose some lower and upper bounds for the coupled-tasks scheduling problem in presence of compatibility constraints according to classical complexity hypothesis ($\mathcal{P} \neq \mathcal{NP}$,…
The graph coloring problem asks for an assignment of the minimum number of distinct colors to vertices in an undirected graph with the constraint that no pair of adjacent vertices share the same color. The problem is a thoroughly studied…
Motivated by modern parallel computing applications, we consider the problem of scheduling parallel-task jobs with heterogeneous resource requirements in a cluster of machines. Each job consists of a set of tasks that can be processed in…
This paper addresses the incompatible case of parallel batch scheduling, where compatible jobs belong to the same family, and jobs from different families cannot be processed together in the same batch. The state-of-the-art constraint…
This paper deals with the complexity of some natural graph problems when parametrized by {measures that are restrictions of} clique-width, such as modular-width and neighborhood diversity. The main contribution of this paper is to introduce…
We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are…
The problem of scheduling conflicting jobs on parallel machines consists in assigning a set of jobs to a set of machines so that no two conflicting jobs are allocated to the same machine, and the maximum processing time among all machines…
Many hard graph problems can be solved efficiently when restricted to graphs of bounded treewidth, and more generally to graphs of bounded clique-width. But there is a price to be paid for this generality, exemplified by the four problems…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
In this paper, we study the parameterized complexity of several variants of scheduling with precedence constraints between jobs. Namely, we consider the single machine setting with delay values on top of the precedence constraints. Such…
In this paper we consider the problem of scheduling on parallel machines with a presence of incompatibilities between jobs. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of…
In the constrained planarity setting, we ask whether a graph admits a planar drawing that additionally satisfies a given set of constraints. These constraints are often derived from very natural problems; prominent examples are Level…
A square coloring of a graph $G$ is a coloring of the square $G^2$ of $G$, that is, a coloring of the vertices of $G$ such that any two vertices that are at distance at most $2$ in $G$ receive different colors. We investigate the complexity…
Temporal graphs have been recently introduced to model changes to a given network that occur throughout a fixed period of time. The Temporal $\Delta$ Clique problem, that generalizes the well known Clique problem to temporal graphs, has…
We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…