Related papers: Bandwidth reduction in rectalgular grids

We show that it is NP-hard to distinguish graphs of linear mim-width at most 1211 from graphs of sim-width at least 1216. This implies that Mim-Width, Sim-Width, One-Sided Mim-Width, and their linear counterparts are all paraNP-complete,…

Bifiltered graphs are a versatile tool for modelling relations between data points across multiple grades of a two-dimensional scale. They are especially popular in topological data analysis, where the homological properties of the induced…

With the rapid proliferation of Internet of Things and intelligent edge devices, there is an increasing need for implementing machine learning algorithms, including deep learning, on resource-constrained mobile embedded devices with limited…

The electronic band structure of atomically thin semiconductors can be tuned by the application of a perpendicular electric field. The principle was demonstrated experimentally shortly after the discovery of graphene by opening a finite…

For each natural number $n$ we determine, both asymptotically and exactly, the maximum number of edges an induced subgraph of order $n$ of the $d$-dimension a grid graph ${\ints}^d$ can have. The asymptotic bound is obtained by using a…

It is shown that every orthogonal terrain, i.e., an orthogonal (right-angled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single non-overlapping piece…

A two-dimensional \emph{grid} is a set $\Gnm = [n]\times[m]$. A grid $\Gnm$ is \emph{$c$-colorable} if there is a function $\chi_{n,m}: \Gnm \to [c]$ such that there are no rectangles with all four corners the same color. We address the…

An $N$-dimensional parallelepiped will be called a bar if and only if there are no more than $k$ different numbers among the lengths of its sides (the definition of bar depends on $k$). We prove that a parallelepiped can be dissected into…

In this short article, we consider a problem about $2$-partition of the vertices of a graph. If a graph admits such a partition into some 'small' graphs, then the number of edges cross an arbitrary cut of the graph $e(S,S^{c})$ has a nice…

In the millimeter wave (30-300 GHz) and Terahertz (0.1-10 THz) frequency bands, high spreading loss and molecular absorption often limit the signal transmission distance and coverage range. In this paper, four directions to tackle the…

The unit-distance graph on the $n$-dimensional integer lattice $\mathbb{Z}^n$ is called the $n$-dimensional grid. We attempt to maximize the girth of a $k$-regular (possibly induced) subgraph of the $n$-dimensional grid, and provide…

This article present a new method to reconstruct slowly varying width defects in 2D waveguides using one-side section measurements at locally resonant frequencies. At these frequencies, locally resonant modes propagate in the waveguide up…

By a well known result the treewidth of k-outerplanar graphs is at most 3k-1. This paper gives, besides a rigorous proof of this fact, an algorithmic implementation of the proof, i.e. it is shown that, given a k-outerplanar graph G, a tree…

It is well known that a graph with $m$ edges can be made triangle-free by removing (slightly less than) $m/2$ edges. On the other hand, there are many classes of graphs which are hard to make triangle-free in the sense that it is necessary…

All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact…

The triangle removal lemma states that a simple graph with o(n^3) triangles can be made triangle-free by removing o(n^2) edges. It is natural to ask if this widely used result can be extended to multi-graphs (or equivalently, weighted…

We give a complete determination of the exact optimal worst-case repair bandwidth and repair I/O for linear exact repair of $(n,n-2,2)$ MDS array codes over every finite field $\mathbb{F}_q$ and for every admissible code length $3\le n\le…

In many applications, it is needed to change the topology of a tensor network directly and without approximation. This work will introduce a general scheme that satisfies these needs. We will describe the procedure by two examples and show…

We study the parameterized complexity of the $s$-Club Cluster Edge Deletion problem: Given a graph $G$ and two integers $s \ge 2$ and $k \ge 1$, is it possible to remove at most $k$ edges from $G$ such that each connected component of the…

We consider the number of vertices that must be removed from a graph G in order that the remaining subgraph has no component with more than k vertices. Our principal observation is that, if G is a sparse random graph or a random regular…