Related papers: On Connectedness of Solutions to Integer Linear Sy…
A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used…
A row and a column of two linear relations in Hilbert spaces are presented respectively as a sum and an intersection of two linear relations. As an application, necessary and sufficient conditions for the adjoint of a column to be a row are…
In this paper, we show how a resource allocation problem can be solved through Integer Linear Programming (ILP). A detailed illustrative example is presented, together with an exhaustive overview of the mathematical model. The size of the…
A graph is \emph{hamiltonian-connected} if every pair of vertices can be connected by a hamiltonian path, and it is \emph{hamiltonian} if it contains a hamiltonian cycle. We construct families of non-hamiltonian graphs for which the ratio…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
A system of linear equations is normally understood as a linear mapping between two vector spaces. However, most direct solutions (e.g., QR, LU, ...) rely on the inelegant approach of back-substitution: a significant departure from such a…
IFS fractals - the attractors of Iterated Function Systems - have motivated plenty of research to date, partly due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design…
In a recent paper, a distributed algorithm was proposed for solving linear algebraic equations of the form $Ax = b$ assuming that the equation has at least one solution. The equation is presumed to be solved by $m$ agents assuming that each…
We define observability and detectability for linear switching systems as the possibility of reconstructing and respectively of asymptotically reconstructing the hybrid state of the system from the knowledge of the output for a suitable…
In this paper, we consider the iterative solution of linear algebraic equations under the condition that matrix-vector products with the coefficient matrix are computed only partially. At the same time, non-computed entries are set to…
We propose a combinatorial optimisation model called Limited Query Graph Connectivity Test. We consider a graph whose edges have two possible states (On/Off). The edges' states are hidden initially. We could query an edge to reveal its…
The general setting of this work is the constraint-based synthesis of termination arguments. We consider a restricted class of programs called lasso programs. The termination argument for a lasso program is a pair of a ranking function and…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
Graph drawing addresses the problem of finding a layout of a graph that satisfies given aesthetic and understandability objectives. The most important objective in graph drawing is minimization of the number of crossings in the drawing, as…
Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over a field $K$, and let $A$ be a finitely generated standard graded $S$-algebra. We show that if the defining ideal of $A$ has a quadratic initial ideal, then all the graded components of…
A combinatorial criterion for the edge ring of a finite connected graph to satisfy Serre's condition R_1 is studied.
Network reliability is the probability that a dynamical system composed of discrete elements interacting on a network will be found in a configuration that satisfies a particular property. We introduce a new reliability property, Ising…
Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…
Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class…
A consistent path system in a graph $G$ is an intersection-closed collection of paths, with exactly one path between any two vertices in $G$. We call $G$ metrizable if every consistent path system in it is the system of geodesic paths…