Related papers: A fast, large-scale optimal transport algorithm fo…
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…
We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs. Given two probability measures supported on a discrete grid with n…
A frame is a generalization of a basis of a vector space to a redundant overspanning set whose vectors are linearly dependent. Frames find applications in signal processing and quantum information theory. We present a genetic algorithm that…
We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of…
In this paper, we study the problem of moving $n$ sensors on a line to form a barrier coverage of a specified segment of the line such that the maximum moving distance of the sensors is minimized. Previously, it was an open question whether…
In this paper we consider several problems concerning packet routing in distributed systems. Each problem is formulated using terms from Graph Theory and for each problem we present efficient, novel, algorithmic techniques for computing…
Sequential robot manipulation tasks require finding collision-free trajectories that satisfy geometric constraints across multiple object interactions in potentially high-dimensional configuration spaces. Solving these problems in real-time…
Developing a contemporary optimal transport (OT) solver requires navigating trade-offs among several critical requirements: GPU parallelization, scalability to high-dimensional problems, theoretical convergence guarantees, empirical…
We describe three algorithms for generating binary-valued holograms. Our methods are optimised for producing large arrays of tightly focussed optical tweezers for trapping particles. Binary-valued holograms allow us to use a digital mirror…
The constrained path optimization (CPO) problem takes the following input: (a) a road network represented as a directed graph, where each edge is associated with a "cost" and a "score" value; (b) a source-destination pair and; (c) a budget…
We present a centralized algorithmic framework for solving multi-robot path planning problems in general, two-dimensional, continuous environments while minimizing globally the task completion time. The framework obtains high levels of…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
This paper presents a computationally efficient optimization algorithm for solving nonconvex optimal control problems that involve discrete logic constraints. Traditional solution methods for these constraints require binary variables and…
Motion planning is a key aspect of robotics. A common approach to address motion planning problems is trajectory optimization. Trajectory optimization can represent the high-level behaviors of robots through mathematical formulations.…
In this paper, we give a faster width-dependent algorithm for mixed packing-covering LPs. Mixed packing-covering LPs are fundamental to combinatorial optimization in computer science and operations research. Our algorithm finds a $1+\eps$…
Variational quantum eigensolver ans\"atze hold considerable promise for ground-state energy calculations on near-term quantum hardware, yet most promising ansatz designs currently strongly depend on how well the molecular orbital basis…
Existing Simultaneous Localization and Mapping (SLAM) approaches are limited in their scalability due to growing map size in long-term robot operation. Moreover, processing such maps for localization and planning tasks leads to the…
By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…
Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…
Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…