Related papers: Topological complexity of a map
In this paper we determine the topological complexity of configuration spaces of graphs which are not necessarily trees, which is a crucial assumption in previous results. We do this for two very different classes of graphs: fully…
We survey two decades of work on the (sequential) topological complexity of configuration spaces of graphs (ordered and unordered), aiming to give an account that is unifying, elementary, and self-contained. We discuss the traditional…
We give simple upper bounds for rational sectional category and use them to compute invariants of the type of Farber's topological complexity of rational spaces. In particular we show that the sectional category of formal morphisms reaches…
Autonomous navigation of a mobile robot is a challenging task which requires ability of mapping, localization, path planning and path following. Conventional mapping methods build a dense metric map like an occupancy grid, which is affected…
Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…
We establish sharp upper bounds for the topological complexity of motion planning problem in spaces with small fundamental group, i.e. when it is finite of small order or has small cohomological dimension.
We introduce the effectual topological complexity (ETC) of a $G$-space $X$. This is a $G$-equivariant homotopy invariant sitting in between the effective topological complexity of the pair $(X,G)$ and the (regular) topological complexity of…
In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these…
Soft robot are celebrated for their propensity to enable compliant and complex robot-environment interactions. Soft robotic manipulators, or slender continuum structure robots have the potential to exploit these interactions to enable new…
We study the effect of topology variation on the dynamic behavior of a system with local update rules. We implement one-dimensional binary cellular automata on graphs with various topologies by formulating two sets of degree-dependent…
One of the most basic, longstanding open problems in the theory of dynamical systems is whether reachability is decidable for one-dimensional piecewise affine maps with two intervals. In this paper we prove that for injective maps, it is…
The \emph{Continuity Problem} is the question whether effective operators are continuous, where an effective operator $F$ is a function on a space of constructively given objects $x$, defined by mapping construction instructions for $x$ to…
This paper deals with the classical problem of exploring a ring by a cohort of synchronous robots. We focus on the perpetual version of this problem in which it is required that each node of the ring is visited by a robot infinitely often.…
We initiate the study of the parameterized complexity of the {\sc Collective Graph Exploration} ({\sc CGE}) problem. In {\sc CGE}, the input consists of an undirected connected graph $G$ and a collection of $k$ robots, initially placed at…
In the communication systems domain, constructing and maintaining network topologies via topology control (TC) algorithms is an important cross-cutting research area. Network topologies are usually modeled using attributed graphs whose…
We study the higher (or sequential) topological complexity $\mathrm{TC}_s$ of manifolds with abelian fundamental group. We give sufficient conditions for $\mathrm{TC}_s$ to be non-maximal in both the orientable and non-orientable cases. In…
We present a simple and easy-to-implement algorithm to detect plan infeasibility in kinematic motion planning. Our method involves approximating the robot's configuration space to a discrete space, where each degree of freedom has a finite…
We compute the topological complexity of Eilenberg-Mac Lane spaces associated to the group of automorphisms of a finitely generated free group which act by conjugation on a given basis, and to certain subgroups.
We survey results on the topological complexity of classical configuration spaces of distinct ordered points in orientable surfaces and related spaces, including certain orbit configuration spaces and Eilenberg-Mac Lane spaces associated to…
A visualized graph is a powerful tool for data analysis and synthesis tasks. In this case, the task of visualization constitutes not only in displaying vertices and edges according to the graph representation, but also in ensuring that the…