11 papers
Polyomino Nets Covering Three Different Boxes of Area 106 and Related Results
Erik D. Demaine, Jenny Diomidova, Nicole Jacobus +5
We present new results for polyomino nets that fold into 2 and 3 different cuboids through a computer search. The main result is the finding of 40 nets that fold into all three dif…
Planar Graph Orientation Frameworks, Applied to KPlumber and Polyomino Tiling
MIT Hardness Group, Zachary Abel, Erik D. Demaine +3
Given a graph, when can we orient the edges to satisfy local constraints at the vertices, where each vertex specifies which local orientations of its incident edges are allowed? Th…
Undecidability of Tiling with a Tromino
ULB CompGeom Group, Zachary Abel, Hugo Akitaya +6
Given a periodic placement of copies of a tromino (either L or I), we prove co-RE-completeness (and hence undecidability) of deciding whether it can be completed to a plane tiling.…
Pushing Blocks without Fixed Walls via Checkable Gizmos: Push-1 is PSPACE-Complete
MIT Hardness Group, Josh Brunner, Lily Chung +4
We prove PSPACE-completeness of Push-1: given a rectangular grid of 1 x 1 cells, each possibly occupied by a movable block, can a robot move from one specified location to another,…
All Polyhedral Manifolds are Connected by a 2-Step Refolding
Lily Chung, Erik D. Demaine, Jenny Diomidova +4
We prove that, for any two polyhedral manifolds , there is a polyhedral manifold such that share a common unfolding an…
All Polyhedral Manifolds are Connected by a 2-Step Refolding
Lily Chung, Erik D. Demaine, Jenny Diomidova +4
We prove that, for any two polyhedral manifolds , there is a polyhedral manifold such that share a common unfolding and…
Reconfiguration Algorithms for Cubic Modular Robots with Realistic Movement Constraints
NASA Space Robots Team, Josh Brunner, Kenneth C. Cheung +5
We introduce and analyze a model for self-reconfigurable robots made up of unit-cube modules. Compared to past models, our model aims to newly capture two important practical aspec…
Any Regular Polyhedron Can Transform to Another by O(1) Refoldings
Erik D. Demaine, Martin L. Demaine, Jenny Diomidova +3
We show that several classes of polyhedra are joined by a sequence of O(1) refolding steps, where each refolding step unfolds the current polyhedron (allowing cuts anywhere on the…
Strings-and-Coins and Nimstring are PSPACE-complete
Erik D. Demaine, Jenny Diomidova
We prove that Strings-and-Coins -- the combinatorial two-player game generalizing the dual of Dots-and-Boxes -- is strongly PSPACE-complete on multigraphs. This result improves the…
New Results in Sona Drawing: Hardness and TSP Separation
Man-Kwun Chiu, Erik D. Demaine, Jenny Diomidova +6
Given a set of point sites, a sona drawing is a single closed curve, disjoint from the sites and intersecting itself only in simple crossings, so that each bounded region of its co…
Walking through Doors is Hard, even without Staircases: Universality and PSPACE-hardness of Planar Door Gadgets
MIT Gadgets Group, Jeffrey Bosboom, Erik D. Demaine +4
An open-close door gadget has two states and three tunnels that can be traversed by an agent (player, robot, etc.): the "opening" and "closing" tunnels set the gadget's state to op…