Related papers: Rectangular Spiral Galaxies are Still Hard
We show that packing axis-aligned unit squares into a simple polygon $P$ is NP-hard, even when $P$ is an orthogonal and orthogonally convex polygon with half-integer coordinates. It has been known since the early 80s that packing unit…
Let G denote a graph and let K be a subset of vertices that are a set of target vertices of G. The K-terminal reliability of G is defined as the probability that all target vertices in K are connected, considering the possible failures of…
It is shown that compact groups of galaxies (HCGs, ShCGS) are stable formations, in which principal member galaxies together with faint galaxies in their environment rotate in elongated orbits around the common gravitational center of the…
Rikudo is a number-placement puzzle, where the player is asked to complete a Hamiltonian path on a hexagonal grid, given some clues (numbers already placed and edges of the path). We prove that the game is complete for NP, even if the…
Sudoku grids can be thought of as graphs where the vertices are the squares of the grid, and edges join vertices in the same row, column, or sub-grid. A Sudoku puzzle corresponds to a partial proper coloring of the Sudoku graph. We provide…
Whether the spiral structure of galaxies is trailing or leading has been a subject of debate. We present a new spin parity catalog of 146 spiral galaxies that lists the following three pieces of information: whether the spiral structure…
We introduce the notion of a "crystallographic sphere packing," defined to be one whose limit set is that of a geometrically finite hyperbolic reflection group in one higher dimension. We exhibit for the first time an infinite family of…
We prove that the art gallery problem is equivalent under polynomial time reductions to deciding whether a system of polynomial equations over the real numbers has a solution. The art gallery problem is a classical problem in computational…
As a result of our statistical study of 540 edge-on galaxies, we present here the images and preliminary statistical analysis of a sub-sample of 60 galaxies, that were selected to be S-type warped spirals. Computing the average volumic…
We consider the problem of deciding, given a sequence of regions, if there is a choice of points, one for each region, such that the induced polyline is simple or weakly simple, meaning that it can touch but not cross itself. Specifically,…
Circle packings are arrangement of circles satisfying specified tangency requirements. Many problems about packing of circles and spheres occur in nature particularly in material design and protein structure. Surprisingly, little is known…
We prove that path puzzles with complete row and column information--or equivalently, 2D orthogonal discrete tomography with Hamiltonicity constraint--are strongly NP-complete, ASP-complete, and #P-complete. Along the way, we newly…
The spiral galaxies, including our galaxy, are created by the gravito-radiative forces generated by colliding black holes at the center of quasars. The gravito-radiative force is predicted by Einstein's general relativity. A quasar is…
A rep-tile is a polygon that can be dissected into smaller copies (of the same size) of the original polygon. A polyomino is a polygon that is formed by joining one or more unit squares edge to edge. These two notions were first introduced…
We propose an explanation of features of spiral galaxies: spiral arms and observed flat rotation curves, without the presence of an exotic form of matter. The formalism is based on Boltzmanns transport equation for the collisional matter…
Our vision of galaxies has changed significantly since the era of large galaxy surveys like the Sloan, which gave us extensive statistics with millions of galaxies. The Hubble sequence classification described in Chapter 1 still remains…
We analyze the rotation curves of 10 spiral galaxies with a newtonian potential corrected with an extra logarithmic term, using a disc modelization for the spiral galaxies. There is a new constant associated with the extra term in the…
Two planar sets are circularly separable if there exists a circle enclosing one of the sets and whose open interior disk does not intersect the other set. This paper studies two problems related to circular separability. A linear-time…
In this article I extend an earlier study of spiral galaxies in the Sloan Digital Sky Survey (SDSS) to investigate whether the universe has an overall handedness. A preference for spiral galaxies in one sector of the sky to be left-handed…
We analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but…