Related papers: Fractional programming formulation for the vertex …
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
We investigate the possibilities to calculate vector partition functions by means of iterated partial fraction decomposition, as suggested by Beck (2004). Particularly, for an important type of families of rational functions, we describe an…
We introduce a variant of the vertex-distinguishing edge coloring problem, where each edge is assigned a subset of colors. The label of a vertex is the union of the sets of colors on edges incident to it. In this paper we investigate the…
Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite…
A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…
A graph on $n$ vertices is equitably $k$-colorable if it is $k$-colorable and every color is used either $\left\lfloor n/k \right\rfloor$ or $\left\lceil n/k \right\rceil$ times. Such a problem appears to be considerably harder than vertex…
Image segmentation is a fundamental and challenging task in image processing and computer vision. The color image segmentation is attracting more attention due to the color image provides more information than the gray image. In this paper,…
Fixed-parameter algorithms have been successfully applied to solve numerous difficult problems within acceptable time bounds on large inputs. However, most fixed-parameter algorithms are inherently \emph{sequential} and, thus, make no use…
We propose a vector linear programming formulation for a non-stationary, finite-horizon Markov decision process with vector-valued rewards. Pareto efficient policies are shown to correspond to efficient solutions of the linear program, and…
An independent transversal (IT) in a graph with a given vertex partition is an independent set consisting of one vertex in each partition class. Several sufficient conditions are known for the existence of an IT in a given graph with a…
We develop an algorithmic framework for graph colouring that reduces the problem to verifying a local probabilistic property of the independent sets. With this we give, for any fixed $k\ge 3$ and $\varepsilon>0$, a randomised…
We prove that every partial function with finite domain and range can be effectively simulated through sequential colorings of graphs. Namely, we show that given a finite set $S=\{0,1,\ldots,m-1\}$ and a number $n \geq \max\{m,3\}$, any…
A new algorithm for exactly sampling from the set of proper colorings of a graph is presented. This is the first such algorithm that has an expected running time that is guaranteed to be linear in the size of a graph with maximum degree \(…
We consider a stochastic sequence $\xi(m)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. The filtering…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
In this paper, we study the conflict-free coloring of graphs induced by neighborhoods. A coloring of a graph is conflict-free if every vertex has a uniquely colored vertex in its neighborhood. The conflict-free coloring problem is to color…
In the Colored Clustering problem, one is asked to cluster edge-colored (hyper-)graphs whose colors represent interaction types. More specifically, the goal is to select as many edges as possible without choosing two edges that share an…
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…
The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte-Carlo simulations. We critically discuss…
Chromatic polynomials have been studied extensively, giving us results such as the Fundamental Reduction Theorem and closed formulas for the chromatic polynomials of common classes of graphs. Though, none of those extend to the context of…