Related papers: Rational sequential parametrized topological compl…

In this paper, we investigate discrete topological complexity $TC(K)$ introduced for situations where the configuration space possesses a simplicial structure. %Simplicial complexes are well-known and commonly used in programming for…

In this paper, we transfer the problem of measuring navigational complexity in topological spaces to the nearness theory. We investigate the most important component of this problem, the topological complexity number (denoted by TC), with…

The central problem in computational algebraic topology is the computation of the homotopy groups of a given space, represented as a simplicial set. Algorithms have been found which achieve this, but the running times depend on the size of…

In this article algebraic constructions are introduced in order to study the variety defined by a radical parametrization (a tuple of functions involving complex numbers, $n$ variables, the four field operations and radical extractions). We…

Parameterized complexity allows us to analyze the time complexity of problems with respect to a natural parameter depending on the problem. Reoptimization looks for solutions or approximations for problem instances when given solutions to…

In this article, we extend Sullivan's PL de Rham theory to obtain simple algebraic models for the rational homotopy theory of parametrised spectra. This simplifies and complements the results of arXiv:1910.14608, which are based on…

This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…

How hard is it to program $n$ robots to move about a long narrow aisle while making a series of $r-2$ intermediate stops, provided only $w$ of the robots can fit across the width of the aisle? In this paper, we answer this question by…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

In this note we define fibrations of topological stacks and establish their main properties. We prove various standard results about fibrations (fiber homotopy exact sequence, Leray-Serre and Eilenberg-Moore spectral sequences, etc.). We…

We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the…

Finding the Time-Optimal Parameterization of a Path (TOPP) subject to second-order constraints (e.g. acceleration, torque, contact stability, etc.) is an important and well-studied problem in robotics. In comparison, TOPP subject to…

The maximum modularity of a graph is a parameter widely used to describe the level of clustering or community structure in a network. Determining the maximum modularity of a graph is known to be NP-complete in general, and in practice a…

We introduce a framework, twisted parametrized stable homotopy theory, for describing semi-infinite homotopy types. A twisted parametrized spectrum is a section of a bundle whose fibre is the category of spectra. We define these bundles in…

The embedding problem is to decide, given an ordered pair of structures, whether or not there is an injective homomorphism from the first structure to the second. We study this problem using an established perspective in parameterized…

Synchronous dynamic systems are well-established models that have been used to capture a range of phenomena in networks, including opinion diffusion, spread of disease and product adoption. We study the three most notable problems in…

We first study the higher version of the relative topological complexity by using the homotopic distance. We also introduced the generalized version of the relative topological complexity of a topological pair on both the Schwarz genus and…

Conditional differential entropy provides an intuitive measure for relatively ranking time-series complexity by quantifying uncertainty in future observations given past context. However, its direct computation for high-dimensional…

Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparameter persistence modules, marked by wild…

To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an…