Related papers: Sliding Squares in Parallel
We study two well-known reconfiguration problems. Given a start and a target configuration of geometric objects in a polygon, we wonder whether we can move the objects from the start configuration to the target configuration while avoiding…
A new approach to solving a class of rankconstrained semi-definite programming (SDP) problems, which appear in many signal processing applications such as transmit beamspace design in multiple-input multiple-output (MIMO) radar, downlink…
The fastest known algorithms for dealing with structured matrices, in the sense of the displacement rank measure, are randomized. For handling classical displacement structures, they achieve the complexity bounds…
Two seemingly unrelated problems, scheduling a multiclass queueing system and minimizing a submodular function, share a rather deep connection via the polymatroid that is characterized by a submodular set function on the one hand and…
Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem…
Scheduling jobs with given processing times on identical parallel machines so as to minimize their total completion time is one of the most basic scheduling problems. We study interesting generalizations of this classical problem involving…
Our work is motivated by the challenges presented in preparing arrays of atoms for use in quantum simulation. The recently-developed process of loading atoms into traps results in approximately half of the traps being filled. To consolidate…
In this paper, we propose a unified algorithmic framework for solving many known variants of \mds. Our algorithm is a simple iterative scheme with guaranteed convergence, and is \emph{modular}; by changing the internals of a single…
Suppose that we are given two independent sets I_b and I_r of a graph such that |I_b|=|I_r|, and imagine that a token is placed on each vertex in |I_b|. Then, the sliding token problem is to determine whether there exists a sequence of…
We study the problem of scheduling jobs on parallel machines minimizing the total completion time, with each job using exactly one resource. First, we derive fundamental properties of the problem and show that the problem is polynomially…
In this paper, we show that the bundle method can be applied to solve semidefinite programming problems with a low rank solution without ever constructing a full matrix. To accomplish this, we use recent results from randomly sketching…
Suppose that two independent sets $I$ and $J$ of a graph with $\vert I \vert = \vert J \vert$ are given, and a token is placed on each vertex in $I$. The Sliding Token problem is to determine whether there exists a sequence of independent…
Motion planning in high-dimensional space is a challenging task. In order to perform dexterous manipulation in an unstructured environment, a robot with many degrees of freedom is usually necessary, which also complicates its motion…
Parallel processing is a principle which enables simultaneous implementation of anesthesia induction and operating room (OR) turnover with the aim of improving OR utilization. In this article, we study the problem of scheduling surgeries…
Deep learning has been effectively applied to many discrete optimization problems. However, learning-based scheduling on unrelated parallel machines remains particularly difficult to design. Not only do the numbers of jobs and machines…
We introduce a new methodology dubbed ``safe peeling'' to accelerate the resolution of L0-regularized least-squares problems via a Branch-and-Bound (BnB) algorithm. Our procedure enables to tighten the convex relaxation considered at each…
We consider planning problems on a punctured Euclidean spaces, $\mathbb{R}^D - \widetilde{\mathcal{O}}$, where $\widetilde{\mathcal{O}}$ is a collection of obstacles. Such spaces are of frequent occurrence as configuration spaces of robots,…
The number of parameters in large-scale language models based on transformers is gradually increasing, and the scale of computing clusters is also growing. The technology of quickly mobilizing large amounts of computing resources for…
Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…