19 citations · 46 across the 18 of their papers we have counts for
11 papers · 1 filter
Spanning Properties of Theta-Theta-6
Mirela Damian, John Iacono, Andrew Winslow
We show that, unlike the Yao-Yao graph , the Theta-Theta graph defined by six cones is a spanner for sets of points in convex position. We also show that, for sets of…
Optimal Staged Self-Assembly of General Shapes
Cameron Chalk, Eric Martinez, Robert Schweller +3
We analyze the number of tile types , bins , and stages necessary to assemble squares and scaled shapes in the staged tile assembly model. For squar…
Size-Dependent Tile Self-Assembly: Constant-Height Rectangles and Stability
Sándor P. Fekete, Robert T. Schweller, Andrew Winslow
We introduce a new model of algorithmic tile self-assembly called size-dependent assembly. In previous models, supertiles are stable when the total strength of the bonds between an…
A Quasilinear-Time Algorithm for Tiling the Plane Isohedrally with a Polyomino
Stefan Langerman, Andrew Winslow
A plane tiling consisting of congruent copies of a shape is isohedral provided that for any pair of copies, there exists a symmetry of the tiling mapping one copy to the other. We…
An Optimal Algorithm for Tiling the Plane with a Translated Polyomino
Andrew Winslow
We give a -time algorithm for determining whether translations of a polyomino with edges can tile the plane. The algorithm is also a -time algorithm for enumerating…
Covering Folded Shapes
Oswin Aichholzer, Greg Aloupis, Erik D. Demaine +6
Can folding a piece of paper flat make it larger? We explore whether a shape must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary f…