**Authors:** MIT CompGeom Group, Hugo A. Akitaya, Erik D. Demaine, Fabian Frei, Stefan Langerman, Anna Lubiw, Joseph O'Rourke Research on Dürer's problem focuses on edge unfoldings of convex polyhedra that avoid overlap. We invert the goal and find unfoldings that overlap at some point to any given thickness t. We have two main results. The first is that, if we allow unfolding cuts that do not follow polyhedron edges, then there is a convex polyhedron that can unfold with overlap of any given thickness. The second result is that for any given thickness, there is a convex polyhedron with an edge unfolding that overlaps to that thickness.

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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. By contrast, the pr...

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**Authors:** MIT-ULB CompGeom Group, :, Zachary Abel, Hugo Akitaya, Lily Chung, Erik D. Demaine, Jenny Diomidova, Della Hendrickson, Stefan Langerman, Jayson Lynch 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. By contrast, the problem becomes decidable if the initial placement is finite, or if the tile is a domino instead of a tromino (in any dimension). As a consequence, tiling a given periodic subset of the plane with a given tromino (L or I) is co-RE-complete. We also prove co-RE-completeness of tiling the entire plane with two polyominoes (one of which is disconnected and the other of which has constant size), and of tiling 3D space with two connected polycubes (one of which has constant size). If we restrict to tiling by translation only (no rotation), then we obtain co-RE-completeness with one more tile: two trominoes for a periodic subset of 2D, three polyominoes for the 2D plane, and three connected polycubes for 3D space. Along the way, we prove several new complexity and algorithmic results about periodic (infinite) graphs. Notably, we prove that Periodic Planar (1-in-)3SAT-3, 3DM, and Graph Orientation are co-RE-complete in 2D and PSPACE-complete in 1D; we extend basic results in graph drawing to 2D periodic graphs; and we give a polynomial-time algorithm for perfect matching in bipartite periodic graphs.

**Authors:** Hugo A. Akitaya, Greg Aloupis, Ahmad Biniaz, Prosenjit Bose, Jean-Lou De Carufel, Cyril Gavoille, John Iacono, Linda Kleist, Michiel Smid, Diane Souvaine, Leonidas Theocharous A covering path for a finite set $P$ of points in the plane is a polygonal path such that every point of $P$ lies on a segment of the path. The vertices of the path need not be at points of $P$. A covering path is plane if its segments do not cross each other. Let $\pi(n)$ be the minimum number such that every set of $n$ points in the plane admits a plane covering path with at most $\pi(n)$ segments. We prove that $\pi(n)\le \lceil6n/7\rceil$. This improves the previous best-known upper bound of $\lceil 21n/22\rceil$, due to Biniaz (SoCG 2023). Our proof is constructive and yields a simple $O(n\log n)$-time algorithm for computing a plane covering path.

**Authors:** Hugo Akitaya, Matias Korman, Frederick Stock A configuration of $n$ unit-cube-shaped \textit{modules} (or \textit{robots}) is a lattice-aligned placement of the $n$ modules so that their union is face-connected. The reconfiguration problem aims at finding a sequence of moves that reconfigures the modules from one given configuration to another. The sliding cube model (in which modules are allowed to slide over the face or edge of neighboring modules) is one of the most studied theoretical models for modular robots. In the sliding cubes model we can reconfigure between any two shapes in $O(n^2)$ moves ([Abel \textit{et al.} SoCG 2024]). If we are interested in a reconfiguration algorithm into a \textit{compact configuration}, the number of moves can be reduced to the sum of coordinates of the input configuration (a number that ranges from $\Omega(n^{4/3})$ to $O(n^2)$, [Kostitsyna \textit{et al.} SWAT 2024]). We introduce a new algorithm that combines both universal reconfiguration and an input-sensitive bound on the sum of coordinates of both configurations, with additional advantages, such as $O(1)$ amortized computation per move.

**Authors:** Hugo Akitaya, Matias Korman, Frederick Stock A configuration of $n$ unit-cube-shaped \textit{modules} (or \textit{robots}) is a lattice-aligned placement of the $n$ modules so that their union is face-connected. The reconfiguration problem aims at finding a sequence of moves that reconfigures the modules from one given configuration to another. The sliding cube model (in which modules are allowed to slide over the face or edge of neighboring modules) is one of the most studied theoretical models for modular robots. In the sliding cubes model we can reconfigure between any two shapes in $O(n^2)$ moves ([Abel \textit{et al.} SoCG 2024]). If we are interested in a reconfiguration algorithm into a \textit{compact configuration}, the number of moves can be reduced to the sum of coordinates of the input configuration (a number that ranges from $\Omega(n^{4/3})$ to $O(n^2)$, [Kostitsyna \textit{et al.} SWAT 2024]). We introduce a new algorithm that combines both universal reconfiguration and an input-sensitive bound on the sum of coordinates of both configurations, with additional advantages, such as $O(1)$ amortized computation per move.

**Authors:** Hugo Akitaya, Matias Korman, Frederick Stock A configuration of $n$ unit-cube-shaped \textit{modules} (or \textit{robots}) is a lattice-aligned placement of the $n$ modules so that their union is face-connected. The reconfiguration problem aims at finding a sequence of moves that reconfigures the modules from one given configuration to another. The sliding cube model (in which modules are allowed to slide over the face or edge of neighboring modules) is one of the most studied theoretical models for modular robots. In the sliding cubes model we can reconfigure between any two shapes in $O(n^2)$ moves ([Abel \textit{et al.} SoCG 2024]). If we are interested in a reconfiguration algorithm into a \textit{compact configuration}, the number of moves can be reduced to the sum of coordinates of the input configuration (a number that ranges from $\Omega(n^{4/3})$ to $O(n^2)$, [Kostitsyna \textit{et al.} SWAT 2024]). We introduce a new algorithm that combines both universal reconfiguration and an input-sensitive bound on the sum of coordinates of both configurations, with additional advantages, such as $O(1)$ amortized computation per move.

**Authors:** Hugo Akitaya, Matias Korman, Frederick Stock A configuration of $n$ unit-cube-shaped \textit{modules} (or \textit{robots}) is a lattice-aligned placement of the $n$ modules so that their union is face-connected. The reconfiguration problem aims at finding a sequence of moves that reconfigures the modules from one given configuration to another. The sliding cube model (in which modules are allowed to slide over the face or edge of neighboring modules) is one of the most studied theoretical models for modular robots. In the sliding cubes model we can reconfigure between any two shapes in $O(n^2)$ moves ([Abel \textit{et al.} SoCG 2024]). If we are interested in a reconfiguration algorithm into a \textit{compact configuration}, the number of moves can be reduced to the sum of coordinates of the input configuration (a number that ranges from $\Omega(n^{4/3})$ to $O(n^2)$, [Kostitsyna \textit{et al.} SWAT 2024]). We introduce a new algorithm that combines both universal reconfiguration and an input-sensitive bound on the sum of coordinates of both configurations, with additional advantages, such as $O(1)$ amortized computation per move.

Welp, we're right into another fantasy anime and.... wait, that's the title? OK, I'm willing to go around with this. Something about it shows some promise. And maybe something slightly different. This is The Shy Hero and the Assassin Princesses. Director: Noriaki Akitaya Series Composition: Michiko Yokote Music: Shun Narita Original creator: Norishiro-chan Yukiji Setsuda…

Auf dem offiziellen X-Account der Anime-Adaption von »The Shy Hero and the Assassin Princesses« (jap.: »Kizetsu Yuusha to Ansatsu Hime«) wurde heute ein neuer Trailer veröffentlicht, in dem der Opening-Song vorgestellt wird. Das Video findet ihr unten. Simulcast bei Crunchyroll »The Shy Hero and the Assassin Princesses« entsteht unter der Regie von Noriaki Akitaya (»Ayakashi […] Der Beitrag Neuer Trailer zu »The Shy Hero and the Assassin Princesses« erschien zuerst auf Anime2You.