Arne Schmidt

New Geometric Algorithms for Fully Connected Staged Self-Assembly

We consider staged self-assembly systems, in which square-shaped tiles can be added to bins in several stages. Within these bins, the tiles may connect to each other, depending on the glue types of their edges. Previous work by Demaine et al. showed that a relatively small number of tile types suffices to produce arbitrary shapes in this model. However, these constructions were only based on a spanning tree of the geometric shape, so they did not produce full connectivity of the underlying grid graph in the case of shapes with holes; designing fully connected assemblies with a polylogarithmic number of stages was left as a major open problem. We resolve this challenge by presenting new systems for staged assembly that produce fully connected polyominoes in

Don’t Rock the Boat: Algorithms for Balanced Dynamic Loading and Unloading

\mathcal {O}\log ^2 n

Area- and Boundary-Optimal Polygonalization of Planar Point Sets

Olog2n stages, for various scale factors and temperature

Computing nonsimple polygons of minimum perimeter

\tau =2

CADbots: Algorithmic Aspects of Manipulating Programmable Matter with Finite Automata

i¾?=2 as well as