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In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
The article explores an encoding and structural information processing approach using sparse bit vectors and fixed-length linear vectors. The following are presented: a discrete method of speculative stochastic dimensionality reduction of…
Binary relations are commonly used in Computer Science for modeling data. In addition to classical representations using matrices or lists, some compressed data structures have recently been proposed to represent binary relations in compact…
An algorithm for robot formation path planning is presented in this paper. Given a map of the working environment, the algorithm finds a path for a formation taking into account possible split of the formation and its consecutive merge. The…
We explore in this paper a novel approach that builds an overapproximation of the state space of preemptive real time systems. Our graph construction extends the expression of a class to the time distance system that encodes the…
Simplicial partitions are a fundamental structure in computational geometry, as they form the basis of optimal data structures for range searching and several related problems. Current algorithms are built on very specific spatial…
This paper develops an algorithm that guides a multi-robot system in an unknown environment in search of fixed targets. The area to be scanned contains an unknown number of convex obstacles of unknown size and shape. The algorithm covers…
Aiming for accurate estimation of system reliability of load-sharing systems, a flexible model for such systems is constructed by approximating the cumulative hazard functions of component lifetimes using piecewise linear functions. The…
Trajectory planning for mobile robots in cluttered environments remains a major challenge due to narrow passages, where conventional methods often fail or generate suboptimal paths. To address this issue, we propose the adaptive trajectory…
This paper considers trajectory planning for a mobile robot which persistently relays data between pairs of far-away communication nodes. Data accumulates stochastically at each source, and the robot must move to appropriate positions to…
Constrained motion planning is a common but challenging problem in robotic manipulation. In recent years, data-driven constrained motion planning algorithms have shown impressive planning speed and success rate. Among them, the latent…
Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…
In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map…
In this paper, we proposes the construction methods of sliced space-filling design when the quantitative factors are mixture components. Leveraging the representative points framework for distribution and energy distance decomposition…
Key to structured prediction is exploiting the problem structure to simplify the learning process. A major challenge arises when data exhibit a local structure (e.g., are made by "parts") that can be leveraged to better approximate the…
This paper presents a distributed method for robots moving in rigid formations while ensuring probabilistic collision avoidance between the robots. The formation is parametrised through the transformation of a base configuration. The robots…
Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which…
This paper presents a novel planning method that achieves navigation of multi-robot formations in cluttered environments, while maintaining the formation throughout the robots motion. The method utilises a decentralised approach to find…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in $n-$dimensional space. It is a non-separable approximation, as it is…
Using the notion of contiguity of simplicial maps, we adapt Farber's topological complexity to the realm of simplicial complexes. We show that, for a finite simplicial complex $K$, our discretized concept recovers the topological complexity…