Related papers: Convex Hull Formation for Programmable Matter
In this work, we study theoretical models of \emph{programmable matter} systems. The systems under consideration consist of spherical modules, kept together by magnetic forces and able to perform two minimal mechanical operations (or…
We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…
Necessary and sufficient conditions for the square-integrability of recently proposed unbiased estimators are established. A geometric characterization of a distribution that optimizes the performance of these estimators is given. An…
Several physical systems in condensed matter have been modeled approximating their constituent particles as hard objects. The hard spheres model has been indeed one of the cornerstones of the computational and theoretical description in…
For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a…
In a self-organizing particle system, an abstraction of programmable matter, simple computational elements called particles with limited memory and communication self-organize to solve system-wide problems of movement, coordination, and…
In this paper we present algorithms for collective construction systems in which a large number of autonomous mobile robots trans- port modular building elements to construct a desired structure. We focus on building block structures…
Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given…
We consider a repulsion actuator located in an $n$-sided convex environment full of point particles. When the actuator is activated, all the particles move away from the actuator. We study the problem of gathering all the particles to a…
Concerning huge-scale aggregative convex programming of a linear objective subject to the affine constraints of equality and inequality and the quadratic constraints of inequality, convex and aggregatively computable, an algorithm is…
We contribute results for a set of fundamental problems in the context of programmable matter by presenting algorithmic methods for evaluating and manipulating a collective of particles by a finite automaton that can neither store…
In the preprocessing framework one is given a set of regions that one is allowed to preprocess to create some auxiliary structure such that when a realization of these regions is given, consisting of one point per region, this auxiliary…
We present and rigorously analyze the behavior of a distributed, stochastic algorithm for separation and integration in self-organizing particle systems, an abstraction of programmable matter. Such systems are composed of individual…
Estimating the volume of a convex body is a central problem in convex geometry and can be viewed as a continuous version of counting. We present a quantum algorithm that estimates the volume of an $n$-dimensional convex body within…
We give compact extended formulations for the packing and partitioning orbitopes (with respect to the full symmetric group) described and analyzed in (Kaibel and Pfetsch, 2008). These polytopes are the convex hulls of all 0/1-matrices with…
Self-assembly refers to the process by which small, simple components mix and combine to form complex structures using only local interactions. Designed as a hybrid between tile assembly models and cellular automata, the Tile Automata (TA)…
We propose a family of recursive cutting-plane algorithms to solve feasibility problems with constrained memory, which can also be used for first-order convex optimization. Precisely, in order to find a point within a ball of radius…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
In this paper, we present two deterministic leader election algorithms for programmable matter on the face-centered cubic grid. The face-centered cubic grid is a 3-dimensional 12-regular infinite grid that represents an optimal way to pack…
Chan [JACM, 2010] gave a data structure for maintaining the convex hull of a dynamic set of 3D points under insertions and deletions, supporting extreme-point queries. Subsequent refinements by Kaplan, Mulzer, Roditty, Seiferth, and Sharir…