Related papers: Optimal Algorithms for Separating a Polyhedron fro…
In the moldable job scheduling problem one has to assign a set of $n$ jobs to $m$ machines, in order to minimize the time it takes to process all jobs. Each job is moldable, so it can be assigned not only to one but any number of the equal…
In a multi-robot system, a number of autonomous robots would sense, communicate, and decide to move within a given domain to achieve a common goal. In this paper, we consider a new variant of the pursuit-evasion problem in which the robots…
We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged at vertices that can be folded in the plane continuously…
We provide an algorithm for unfolding the surface of any orthogonal polyhedron that falls into a particular shape class we call Manhattan Towers, to a nonoverlapping planar orthogonal polygon. The algorithm cuts along edges of a 4x5x1…
The exact complexity of geometric cuts and bisections is the longstanding open problem including even the dimension one. In this paper, we resolve this problem for dimension one (the real line) by designing an exact polynomial time…
A wide variety of optimization techniques, both exact and heuristic, tend to be biased samplers. This means that when attempting to find multiple uncorrelated solutions of a degenerate Boolean optimization problem a subset of the solution…
Partitioning large machine learning models across distributed accelerator systems is a complex process, requiring a series of interdependent decisions that are further complicated by internal sharding ambiguities. Consequently, existing…
Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions, developing models for interface and grain boundary structures. In…
Planning motions for two robot arms to move an object collaboratively is a difficult problem, mainly because of the closed-chain constraint, which arises whenever two robot hands simultaneously grasp a single rigid object. In this paper, we…
We study the problem of ordered stabbing of $n$ balls (of arbitrary and possibly different radii, no ball contained in another) in $\mathbb{R}^d$, $d \geq 3$, with either a directed line segment or a (directed) polygonal curve. Here, the…
Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
Liquid crystal elastomers represent a novel class of programmable shape-transforming materials whose shape change trajectory is encoded in the material's nematic director field. Using three-dimensional nonlinear finite element…
The machining process is the most common method for metal cutting, and especially in the finishing of machined parts. In modern industry the goal of production is to manufacture products at a low cost, with high quality in the shortest…
Product disassembly is a labor-intensive process and is far from being automated. Typically, disassembly is not robust enough to handle product varieties from different shapes, models, and physical uncertainties due to component…
We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds;…
In the past decade, we had developed a series of splitting contraction algorithms for separable convex optimization problems, at the root of the alternating direction method of multipliers. Convergence of these algorithms was studied under…
An orthotube consists of orthogonal boxes (e.g., unit cubes) glued face-to-face to form a path. In 1998, Biedl et al. showed that every orthotube has a grid unfolding: a cutting along edges of the boxes so that the surface unfolds into a…
The ability to place objects in the environment is an important skill for a personal robot. An object should not only be placed stably, but should also be placed in its preferred location/orientation. For instance, a plate is preferred to…
A common task in robotics is unloading identical goods from a tray with rectangular grid structure. This naturally leads to the idea of programming the process at one grid position only and translating the motion to the other grid points,…