Related papers: A polyhedral approach for the Equitable Coloring P…
In this paper, we investigate the impact of the broadcast effect arising in filterless optical networks on the computational complexity of the wavelength assignment problem. We model conflicts using an appropriate interference digraph,…
Let $A(x)=A\_0+x\_1A\_1+...+x\_nA\_n$ be a linear matrix, or pencil, generated by given symmetric matrices $A\_0,A\_1,...,A\_n$ of size $m$ with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a…
Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
We study $\ell$-colourings of $(v,k,\lambda)$-BIBDs (balanced incomplete block designs) where, within each block, one colour is absent and each of the $\ell-1$ other colours appears exactly $\frac{k}{\ell-1}$ times. We establish several…
In this paper we consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states. We show that the design of the optimal measurement that minimizes the probability of an inconclusive result can…
This note is concerned with the CIECAM02 color appearance model and its successor, the CAM16 color appearance model. Several algorithmic flaws are pointed out and remedies are suggested. The resulting color model is algebraically equivalent…
The problem of sampling edge-colorings of graphs with maximum degree $\Delta$ has received considerable attention and efficient algorithms are available when the number of colors is large enough with respect to $\Delta$. Vizing's theorem…
We study the weighted improper coloring problem, a generalization of defective coloring. We present some hardness results and in particular we show that weighted improper coloring is not fixed-parameter tractable when parameterized by…
The partial coloring method is one of the most powerful and widely used method in combinatorial discrepancy problems. However, in many cases it leads to sub-optimal bounds as the partial coloring step must be iterated a logarithmic number…
In this note we give a short overview on symmetry exploiting techniques in three different branches of polyhedral computations: The representation conversion problem, integer linear programming and lattice point counting. We describe some…
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct:…
The cut polytope of a graph arises in many fields. Although much is known about facets of the cut polytope of the complete graph, very little is known for general graphs. The study of Bell inequalities in quantum information science…
The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most one. The equitable chromatic number of a graph $G$, denoted by $\chi_=(G)$, is the minimum $k$ such that $G$ is equitably $k$-colorable. The…
Finding equitable partitions is closely related to the extraction of graph symmetries and of interest in a variety of applications context such as node role detection, cluster synchronization, consensus dynamics, and network control…
In a previous paper, an implementable algorithm was introduced to compute discrete solutions of sweeping processes (i.e. specific first order differential inclusions). The convergence of this numerical scheme was proved thanks to…
Counting problems, determining the number of possible states of a large system under certain constraints, play an important role in many areas of science. They naturally arise for complex disordered systems in physics and chemistry, in…