Related papers: Computing braid groups of graphs with applications…
Quasi-median graphs are a tool commonly used by evolutionary biologists to visualise the evolution of molecular sequences. As with any graph, a quasi-median graph can contain cut vertices, that is, vertices whose removal disconnect the…
To control how a robot moves, motion planning algorithms must compute paths in high-dimensional state spaces while accounting for physical constraints related to motors and joints, generating smooth and stable motions, avoiding obstacles,…
This report presents an algorithm to statically schedule live and strongly connected Marked Graphs (MG). The proposed algorithm computes the best execution where the execution rate is maximal and place sizes are minimal. The proposed…
Prediction of movements is essential for successful cooperation with intelligent systems. We propose a model that integrates organized spatial information as given through the moving body's skeletal structure. This inherent structure is…
Unlike conventional "black-box" transformers with classical self-attention mechanism, we build a lightweight and interpretable transformer-like neural net by unrolling a mixed-graph-based optimization algorithm to forecast traffic with…
We initiate a general theory for analyzing the complexity of motion planning of a single robot through a graph of "gadgets", each with their own state, set of locations, and allowed traversals between locations that can depend on and change…
We define the \emph{visual complexity} of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to…
Planning in robotics is often split into task and motion planning. The high-level, symbolic task planner decides what needs to be done, while the motion planner checks feasibility and fills up geometric detail. It is known however that such…
The gathering over meeting nodes problem requires the robots to gather at one of the pre-defined meeting nodes. This paper investigates the problem with respect to the objective function that minimizes the total number of moves made by all…
We give criteria for deciding whether or not a triangle-free simple graph is the presentation graph of a right-angled Coxeter group that is quasiisometric to some right-angled Artin group, and, if so, producing a presentation graph for such…
We study representations of the braid groups from braiding gapped boundaries of Dijkgraaf-Witten theories and their twisted generalizations, which are (twisted) quantum doubled topological orders in two spatial dimensions. We show that the…
We present a complete framework for fast motion planning of non-holonomic autonomous mobile robots in highly complex but structured environments. Conventional grid-based planners struggle with scalability, while many kinematically-feasible…
We provide a comprehensive systematic method for the numerical computation of elementary braid operations in topological quantum computation (TQC). This {procedure} is systematically applicable to all anyon models, including $SU(2)_k$.…
Safe and efficient crowd navigation for mobile robot is a crucial yet challenging task. Previous work has shown the power of deep reinforcement learning frameworks to train efficient policies. However, their performance deteriorates when…
We consider the problem of connected coordinated motion planning for a large collective of simple, identical robots: From a given start grid configuration of robots, we need to reach a desired target configuration via a sequence of…
Bipartite graphs model the relationship between two disjoint sets of objects. They have a wide range of applications and are often visualized as a 2-layered drawing, where each set of objects is visualized as a set of vertices (points) on…
We consider dataflow architecture for two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We improve the earlier technique of almost continuous program…
Isoperimetric robots are large scale, untethered inflatable robots that can undergo large shape changes, but have only been demonstrated in one 3D shape -- an octahedron. These robots consist of independent triangles that can change shape…
Automated planning is one of the foundational areas of AI. Since no single planner can work well for all tasks and domains, portfolio-based techniques have become increasingly popular in recent years. In particular, deep learning emerges as…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…