Related papers: A Parameterized Algorithm for Flat Folding

Sparse structures are frequently sought when pursuing tractability in optimization problems. They are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present.…

Computing planar orthogonal drawings with the minimum number of bends is one of the most relevant topics in Graph Drawing. The problem is known to be NP-hard, even when we want to test the existence of a rectilinear planar drawing, i.e., an…

We identify a sufficient condition, treewidth-pliability, that gives a polynomial-time algorithm for an arbitrarily good approximation of the optimal value in a large class of Max-2-CSPs parameterised by the class of allowed constraint…

We survey more recent attempts at enumerating the number of mountain-valley assignments that allow a given crease pattern to locally fold flat. In particular, we solve this problem for square twist tessellations and generalize the method…

To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an…

Non-Euclidean origami is a promising technique for designing multistable deployable structures folded from nonplanar developable surfaces. The impossibility of flat foldability inherent to non-Euclidean origami results in two disconnected…

One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic (MSO_2) is fixed-parameter tractable (fpt) on C by linear time parameterized algorithms,…

We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…

Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly…

We develop a framework for applying treewidth-based dynamic programming on graphs with "hybrid structure", i.e., with parts that may not have small treewidth but instead possess other structural properties. Informally, this is achieved by…

Tree-width has been proven to be a useful parameter to design fast and efficient algorithms for intractable problems. However, while tree-width is low on relatively sparse graphs can be arbitrary high on dense graphs. Therefore, we…

In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs…

Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…

Flat electronic bands with tunable structures offer opportunities for the exploitation and manipulation of exotic interacting quantum states. Here, we present a controllable route to construct easily tunable flat bands in folded graphene,…

In the field of parameterized complexity theory, the study of graph width measures has been intimately connected with the development of width-based model checking algorithms for combinatorial properties on graphs. In this work, we…

The concept of kirigami has been extensively utilized to design deployable structures and reconfigurable metamaterials. Despite heuristic utilization of classical kirigami patterns, the gap between complex kirigami tessellations and…

We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the…

Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…

The C-Planarity problem asks for a drawing of a $\textit{clustered graph}$, i.e., a graph whose vertices belong to properly nested clusters, in which each cluster is represented by a simple closed region with no edge-edge crossings, no…

Can folding a piece of paper flat make it larger? We explore whether a shape $S$ must be scaled to cover a flat-folded copy of itself. We consider both single folds and arbitrary folds (continuous piecewise isometries $S\rightarrow R^2$).…