Related papers: Evacuating from ell_p Unit Disks in the Wireless M…
Euclidean Distance Matrix (EDM), which consists of pairwise squared Euclidean distances of a given point configuration, finds many applications in modern machine learning. This paper considers the setting where only a set of anchor nodes is…
Online planning of collision-free trajectories is a fundamental task for robotics and self-driving car applications. This paper revisits collision avoidance between ellipsoidal objects using differentiable constraints. Two ellipsoids do not…
In the paper arXiv:1708.02289 we have introduced new solvability methods for strongly elliptic second order systems in divergence form on a domains above a Lipschitz graph, satisfying $L^p$-boundary data for $p$ near $2$. The main novel…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
Ergodic search enables optimal exploration of an information distribution while guaranteeing the asymptotic coverage of the search space. However, current methods typically have exponential computation complexity in the search space…
Packing problems are an important class of optimization problems. The probably most well-known problem if this type is knapsack and many generalizations of it have been studied in the literature like Two-dimensional Geometric Knapsack…
Learning optimal resource allocation policies in wireless systems can be effectively achieved by formulating finite dimensional constrained programs which depend on system configuration, as well as the adopted learning parameterization. The…
This paper focuses on designing edge-weighted networks, whose robustness is characterized by maximizing algebraic connectivity, or the second smallest eigenvalue of the Laplacian matrix. This problem is motivated by cooperative vehicle…
We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness…
The dispersion problem has been widely studied in computational geometry and facility location, and is closely related to the packing problem. The goal is to locate n points (e.g., facilities or persons) in a k-dimensional polytope, so that…
Given a set ${\cal D}$ of unit disks in the Euclidean plane, we consider (i) the {\it discrete unit disk cover} (DUDC) problem and (ii) the {\it rectangular region cover} (RRC) problem. In the DUDC problem, for a given set ${\cal P}$ of…
Euler k-means (EulerK) first maps data onto the unit hyper-sphere surface of equi-dimensional space via a complex mapping which induces the robust Euler kernel and next employs the popular $k$-means. Consequently, besides enjoying the…
In this work we consider the problem of finding the minimum-weight loop cover of an undirected graph. This combinatorial optimization problem is called 2-matching and can be seen as a relaxation of the traveling salesman problem since one…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
We prove a special case of Erd\H{o}s' unit distance problem using a corollary of the subspace theorem bounding the number of solutions of linear equations from a multiplicative group. We restrict our attention to unit distances coming from…
We study the optimal transport problem on globally hyperbolic spacetimes associated with Orlicz-type Lorentzian cost functions of the form $u \circ \ell$, where $u$ is a suitable monotonically increasing and concave function, and $\ell$ is…
In this paper, we consider the problem of collectively exploring unknown and dynamic environments with a decentralized heterogeneous multi-robot system consisting of multiple units of two variants of a miniature robot. The first variant-a…
The problem of coordination without a priori information about the environment is important in robotics. Applications vary from formation control to search and rescue. This paper considers the problem of search by a group of solitary…
This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities and we prove the…
Motion planning problems for physically-coupled multi-robot systems in cluttered environments are challenging due to their high dimensionality. Existing methods combining sampling-based planners with trajectory optimization produce…