Related papers: Space-Efficient Data Structures for Lattices
With the growing maturity of additive manufacturing, the fabrication of architected or lattice-based metamaterials has become a reality for industrial applications. These materials combine lightweight design with tailored mechanical…
The optimal lattice quantizer is the lattice which minimizes the (dimensionless) second moment $G$. In dimensions $1$ to $8$, it has been proven that the optimal lattice quantizer is one of the classical lattices, or there is good evidence…
We introduce data structures answering queries concerning the occurrences of patterns from a given dictionary $\mathcal{D}$ in fragments of a given string $T$ of length $n$. The dictionary is internal in the sense that each pattern in…
In a capacitated directed graph, it is known that the set of all min-cuts forms a distributive lattice [1], [2]. Here, we describe this lattice as a regular predicate whose forbidden elements can be advanced in constant parallel time after…
Let $\kappa(s,t)$ denote the maximum number of internally disjoint $st$-paths in an undirected graph $G$. We consider designing a compact data structure that answers $k$-bounded node connectivity queries: given $s,t \in V$ return…
Let $\mathcal{D}$ be a collection of $D$ documents, which are strings over an alphabet of size $\sigma$, of total length $n$. We describe a data structure that uses linear space and and reports $k$ most relevant documents that contain a…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
Temporal graphs represent interactions between entities over time. Deciding whether entities can reach each other through temporal paths is useful for various applications such as in communication networks and epidemiology. Previous works…
Set intersection is a fundamental operation in information retrieval and database systems. This paper introduces linear space data structures to represent sets such that their intersection can be computed in a worst-case efficient way. In…
We consider the problem of finding the closest lattice point to a vector in n-dimensional Euclidean space when each component of the vector is available at a distinct node in a network. Our objectives are (i) minimize the communication cost…
We present a $O(n^{\frac{3}{2}})$-time algorithm for the \emph{shortest (diagonal) flip path problem} for \emph{lattice} triangulations with $n$ points, improving over previous $O(n^2)$-time algorithms. For a large, natural class of inputs,…
In the last few years, the amount of collected data, in various computer science applications, has grown considerably. These large volumes of data need to be analyzed in order to extract useful hidden knowledge. This work focuses on…
Modern distributed storage systems offer large capacity to satisfy the exponentially increasing need of storage space. They often use erasure codes to protect against disk and node failures to increase reliability, while trying to meet the…
In this work, we propose a framework to store and manage spatial data, which includes new efficient algorithms to perform operations accepting as input a raster dataset and a vector dataset. More concretely, we present algorithms for…
In this paper, we present a fast algorithm for constructing a concept (Galois) lattice of a binary relation, including computing all concepts and their lattice order. We also present two efficient variants of the algorithm, one for…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
Dynamic or temporal networks enable representation of time-varying edges between nodes. Conventional adjacency-based data structures used for storing networks such as adjacency lists were designed without incorporating time and can thus…
We present a succinct data structure for permutation graphs, and their superclass of circular permutation graphs, i.e., data structures using optimal space up to lower order terms. Unlike concurrent work on circle graphs (Acan et al. 2022),…
Suffix tree (and the closely related suffix array) are fundamental structures capturing all substrings of a given text essentially by storing all its suffixes in the lexicographical order. In some applications, we work with a subset of $b$…
In this paper we study the four-dimensional dominance range reporting problem and present data structures with linear or almost-linear space usage. Our results can be also used to answer four-dimensional queries that are bounded on five…