Related papers: Computing braid groups of graphs with applications…
Multi-mobile robot systems show great advantages over one single robot in many applications. However, the robots are required to form desired task-specified formations, making feasible motions decrease significantly. Thus, it is challenging…
The topological model for quantum computation is an inherently fault-tolerant model built on anyons in topological phases of matter. A key role is played by the braid group, and in this survey we focus on a selection of ways that the…
Path planning for multiple tethered robots is a challenging problem due to the complex interactions among the cables and the possibility of severe entanglements. Previous works on this problem either consider idealistic cable models or…
In this paper, we introduce a new approach for drawing diagrams that have applications in software visualization. Our approach is to use a technique we call confluent drawing for visualizing non-planar diagrams in a planar way. This…
We present an improved algorithm for computing the $4$-edge-connected components of an undirected graph in linear time. The new algorithm uses only elementary data structures, and it is simple to describe and to implement in the pointer…
In this paper we give new presentations of the braid groups and the pure braid groups of a closed surface. We also give an algorithm to solve the word problem in these groups, using the given presentations.
This paper is concerned with problems relevant to motion planning in robotics. Configuration spaces are of practical relevance in designing safe control schemes for robots moving on a track. The topological complexity of a configuration…
We give an algorithm to morph planar graph drawings that achieves small grid size at the expense of allowing a constant number of bends on each edge. The input is an $n$-vertex planar graph and two planar straight-line drawings of the graph…
Robot navigation in crowded pedestrian environments is a well-known challenge and we explore the practical deployment of group-based representations in this setting. Pedestrian groups have been empirically shown to enable a mobile robot's…
Nonlinear programming targets nonlinear optimization with constraints, which is a generic yet complex methodology involving humans for problem modeling and algorithms for problem solving. We address the particularly hard challenge of…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
Graphlet analysis is an approach to network analysis that is particularly popular in bioinformatics. We show how to set up a system of linear equations that relate the orbit counts and can be used in an algorithm that is significantly…
Industrial robots can solve very complex tasks in controlled environments, but modern applications require robots able to operate in unpredictable surroundings as well. An increasingly popular reactive policy architecture in robotics is…
Construction of representations of braid group generators from $N$-state vertex models provide an elegant route to study knot and link invariants. Using such a braid group representation, an algebraic formula for the link invariants was put…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
In robotics, coordinating a group of robots is an essential task. This work presents the communication-constrained multi-agent multi-goal path planning problem and proposes a graph-search based algorithm to address this task. Given a fleet…
Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…
We consider the braid groups $\mathbf{B}_n(X)$ on finite simplicial complexes $X$, which are generalizations of those on both manifolds and graphs that have been studied already by many authors. We figure out the relationships between…
The presence of task constraints imposes a significant challenge to motion planning. Despite all recent advancements, existing algorithms are still computationally expensive for most planning problems. In this paper, we present Constrained…
Exchanging particles on graphs, or more concretely on networks of quantum wires, has been proposed as a means to perform fault tolerant quantum computation. This was inspired by braiding of anyons in planar systems. However, exchanges on a…