Related papers: Efficient Segment Folding is Hard
In the context of multi-domain network slices, multiple domains need to work together to provide a service. The problem of determining which part of the service fits within which domain is referred to as slice partitioning. The partitioning…
It is well known that the set of origami constructible numbers is larger than the classical straight-edge and compass constructible numbers. However, the Huzita-Justin-Hatori origami constructible numbers remain algebraic so that the…
In extension problems of partial graph drawings one is given an incomplete drawing of an input graph $G$ and is asked to complete the drawing while maintaining certain properties. A prominent area where such problems arise is that of…
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 $S\rightarrow R^2$).…
We initiate the study of the following natural geometric optimization problem. The input is a set of axis-aligned rectangles in the plane. The objective is to find a set of horizontal line segments of minimum total length so that every…
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show the surprising fact that it is NP-hard to compute the crossing number of near-planar graphs. A graph is 1-planar if it has a drawing where every…
We give an overview of theoretical and practical aspects of finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of n points in the plane. Both problems are known to be NP-hard and were the…
Cloth detection and manipulation is a common task in domestic and industrial settings, yet such tasks remain a challenge for robots due to cloth deformability. Furthermore, in many cloth-related tasks like laundry folding and bed making, it…
Graph packing and partitioning problems have been studied in many contexts, including from the algorithmic complexity perspective. Consider the packing problem of determining whether a graph contains a spanning tree and a cycle that do not…
Rigid origami is a branch of origami with great potential in engineering applications to deal with rigid-panel folding. One of the challenges is to compactly fold the polyhedra made from rigid facets with a single degree of freedom. In this…
When can a plane graph with prescribed edge lengths and prescribed angles (from among $\{0,180^\circ, 360^\circ$\}) be folded flat to lie in an infinitesimally thin line, without crossings? This problem generalizes the classic theory of…
We show that several problems of compacting orthogonal graph drawings to use the minimum number of rows, area, length of longest edge or total edge length cannot be approximated better than within a polynomial factor of optimal in…
Segmenting an image into multiple components is a central task in computer vision. In many practical scenarios, prior knowledge about plausible components is available. Incorporating such prior knowledge into models and algorithms for image…
An NP-hard problem is considered of intersecting a given set of $n$ straight line segments on the plane with the smallest cardinality set of disks of fixed radii $r>0,$ where the set of segments forms a straight line drawing $G=(V,E)$ of a…
In COCOA 2015, Korman et al. studied the following geometric covering problem: given a set $S$ of $n$ line segments in the plane, find a minimum number of line segments such that every cell in the arrangement of the line segments is…
A set of n segments in the plane may form a Euclidean TSP tour, a tree, or a matching, among others. Optimal TSP tours as well as minimum spanning trees and perfect matchings have no crossing segments, but several heuristics and…
We consider the problem of finding an optimal piecewise linear path (polygonal line) connecting two given points with the possibility of making n turns at some points (the absolute value of each turn angle does not exceed a prescribed…
We investigate the problem of partitioning a rectilinear polygon $P$ with $n$ vertices and no holes % with no holes into rectangles using disjoint line segments drawn inside $P$ under two optimality criteria. In the minimum ink partition,…
Simple closed curves in the plane can be mapped to nontrivial knots under the action of origami foldings that allow the paper to self-intersect. We show all tame knot types may be produced in this manner, motivating the development of a new…
For click-based interactive segmentation methods, reducing the number of clicks required to obtain a desired segmentation result is essential. Although recent click-based methods yield decent segmentation results, we observe that…