Related papers: Decomposing Polygons into Fat Components

The component size of a graph is the maximum number of edges in any connected component of the graph. Given a graph $G$ and two integers $k$ and $c$, $(k,c)$-Decomposition is the problem of deciding whether $G$ admits an edge partition into…

The composition technique is a popular method for excluding polynomial-size problem kernels for NP-hard parameterized problems. We present a new technique exploiting triangle-based fractal structures for extending the range of applicability…

Cylindrical algebraic decomposition is a classical construction in real algebraic geometry. Although there are many algorithms to compute a cylindrical algebraic decomposition, their practical performance is still very limited. In this…

We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a…

We introduce the fatness parameter of a 4-dimensional polytope P, defined as \phi(P)=(f_1+f_2)/(f_0+f_3). It arises in an important open problem in 4-dimensional combinatorial geometry: Is the fatness of convex 4-polytopes bounded? We…

Modern generations of field-programmable gate arrays (FPGAs) allow for partial reconfiguration. In an online context, where the sequence of modules to be loaded on the FPGA is unknown beforehand, repeated insertion and deletion of modules…

We study a generalization of the Set Cover problem called the \emph{Partial Set Cover} in the context of geometric set systems. The input to this problem is a set system $(X, \mathcal{S})$, where $X$ is a set of elements and $\mathcal{S}$…

The p-median problem is a classic discrete location problem with several applications. It aims to open p sites while minimizing the sum of the distances of each client to its nearest open site. We study a Benders decomposition of the most…

We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…

In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…

This paper studies the problem of decomposing a low-rank positive-semidefinite matrix into symmetric factors with binary entries, either $\{\pm 1\}$ or $\{0,1\}$. This research answers fundamental questions about the existence and…

A univariate polynomial f over a field is decomposable if it is the composition f = g(h) of two polynomials g and h whose degree is at least 2. We determine the dimension (over an algebraically closed field) of the set of decomposables, and…

We introduce a concept of minimality for Fano polygons. We show that, up to mutation, there are only finitely many Fano polygons with given singularity content, and give an algorithm to determine the mutation-equivalence classes of such…

Starting from Ritt's classical theorems, we give a survey of results in functional decomposition of polynomials and of applications in Diophantine equations. This includes sufficient conditions for the indecomposability of polynomials, the…

We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…

In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…

We address the problem of soft color segmentation, defined as decomposing a given image into several RGBA layers, each containing only homogeneous color regions. The resulting layers from decomposition pave the way for applications that…

We investigate polymer partitioning from polymer mixtures into nanometer size cavities by formulating an equation of state for a binary polymer mixture assuming that only one (smaller) of the two polymer components can penetrate the cavity.…

Given a set $P$ of points and a set $U$ of axis-parallel unit squares in the Euclidean plane, a minimum ply cover of $P$ with $U$ is a subset of $U$ that covers $P$ and minimizes the number of squares that share a common intersection,…

We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…