Related papers: Constructing unlabelled lattices
Algorithms for node clustering typically focus on finding homophilous structure in graphs. That is, they find sets of similar nodes with many edges within, rather than across, the clusters. However, graphs often also exhibit heterophilous…
In this note, we discuss planar lattices generated by their atoms. We prove that if $L$ is a planar lattice generated by $n$ atoms, then both the left and the right boundaries of $L$ have at most $n+1$ elements. On the other hand, $L$ can…
Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…
We present a new efficient algortithm for construction of linear latent structure (LLS) models. This algorithm reduces a problem of estimation of model parameters to a sequence of problems of linear algebra, which assures a low…
(Im)balance indices can be used to quantify the (im)balance of trees by assigning numerical scores to them. An easy way to generate a new index is to construct a compound index, e.g., a linear combination of established indices. Two of the…
This work provides simple algorithms for multi-class (and multi-label) prediction in settings where both the number of examples n and the data dimension d are relatively large. These robust and parameter free algorithms are essentially…
Given two messages - as linear sequences of letters, it is immediate to determine whether one can be transformed into the other by simple substitution cipher of the letters. On the other hand, if the letters are carried as labels on nodes…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
We consider algorithmic problems motivated by modular robotic reconfiguration in the sliding square model, in which we are given $n$ square-shaped modules in a (labeled or unlabeled) start configuration and need to find a schedule of…
We introduce the extra slow Tamari lattices, a new family of lattices defined on faithfully balanced tableaux. These tableaux arise naturally from the representation theory of type \( A \) quivers, and our construction extends the classical…
We consider the problems of computing maximal palindromes and distinct palindromes in a trie. A trie is a natural generalization of a string, which can be seen as a single-path tree. There is a linear-time offline algorithm to compute…
We present a new algorithm for the design of the connection region between different lattice materials. We solve a Stokes-type topology optimization problem on a narrow morphing region to smoothly connect two different unit cells. The…
The (fast) component-by-component (CBC) algorithm is an efficient tool for the construction of generating vectors for quasi-Monte Carlo rank-1 lattice rules in weighted reproducing kernel Hilbert spaces. We consider product weights, which…
In this paper we describe an approach to construct large extendable collections of vectors in predefined spaces of given dimensions. These collections are useful for neural network latent space configuration and training. For classification…
As demand for Real-Time applications rises among the general public, the importance of enabling large-scale, unbound algorithms to solve conventional problems with low to no latency is critical for product viability. Timer algorithms are…
Listing triangles is a fundamental graph problem with many applications, and large graphs require fast algorithms. Vertex ordering allows the orientation of edges from lower to higher vertex indices, and state-of-the-art triangle listing…
In 2002 Thakare et al.\ counted non-isomorphic lattices on $n$ elements, having nullity up to two. In 2020 Bhavale and Waphare introduced the concept of RC-lattices as the class of all lattices in which all the reducible elements are…
Transductive graph-based semi-supervised learning methods usually build an undirected graph utilizing both labeled and unlabeled samples as vertices. Those methods propagate label information of labeled samples to neighbors through their…
We present algorithms for classification of linear codes over finite fields, based on canonical augmentation and on lattice point enumeration. We apply these algorithms to obtain classification results over fields with 2, 3 and 4 elements.…
A graph has the unique path property UPP_n if there is a unique path of length n between any ordered pair of nodes. This paper reiterates Royle and MacKay's technique for constructing orderly algorithms. We wish to use this technique to…