Related papers: On-the-Fly Array Initialization in Less Space

For nearly six decades, the central open question in the study of hash tables has been to determine the optimal achievable tradeoff curve between time and space. State-of-the-art hash tables offer the following guarantee: If keys/values are…

In an array of N elements, M positions and M elements are "marked". We show how to permute the elements in the array so that all marked elements end in marked positions, in time O(N) (in the standard word-RAM model), deterministically, and…

Given a pattern $P$ and a text $T$, both strings over a binary alphabet, the binary jumbled string matching problem consists in telling whether any permutation of $P$ occurs in $T$. The indexed version of this problem, i.e., preprocessing a…

We consider the problem of maintaining a dynamic set of integers and answering queries of the form: report a point (equivalently, all points) in a given interval. Range searching is a natural and fundamental variant of integer search, and…

For every fixed $d \in \mathbb{N}$, we design a data structure that represents a binary $n \times n$ matrix that is $d$-twin-ordered. The data structure occupies $O_d(n)$ bits, which is the least one could hope for, and can be queried for…

Let $x \in \R$ be given. As we know the, amount of bits needed to binary code $x$ with given accuracy ($h \in \R$) is approximately $ \m_{h}(x) \approx \log_{2}(\max {1, |\frac{x}{h}|}). $ We consider the problem where we should translate…

For a stationary stochastic process $\{X_n\}$ with values in some set $A$, a finite word $w \in A^K$ is called a memory word if the conditional probability of $X_0$ given the past is constant on the cylinder set defined by $X_{-K}^{-1}=w$.…

We develop dynamic dictionaries on the word RAM that use asymptotically optimal space, up to constant factors, subject to insertions and deletions, and subject to supporting perfect-hashing queries and/or membership queries, each operation…

Multi-parameter persistent homology is a recent branch of topological data analysis. In this area, data sets are investigated through the lens of homology with respect to two or more scale parameters. The high computational cost of many…

A predecessor (successor) search finds the largest element $x^-$ smaller than the input string $x$ (the smallest element $x^+$ larger than or equal to $x$, respectively) out of a given set $S$; in this paper, we consider the static case…

The field of succinct data structures has flourished over the last 16 years. Starting from the compressed suffix array (CSA) by Grossi and Vitter (STOC 2000) and the FM-index by Ferragina and Manzini (FOCS 2000), a number of generalizations…

Phase Change Memory (PCM) has rapidly progressed and surpassed Dynamic Random-Access Memory (DRAM) in terms of scalability and standby energy efficiency. Altering a PCM cell's state during writes demands substantial energy, posing a…

The deviation of the observed frequency of a word $w$ from its expected frequency in a given sequence $x$ is used to determine whether or not the word is avoided. This concept is particularly useful in DNA linguistic analysis. The value of…

Extended variants of the recently introduced spread unary coding are described. These schemes, in which the length of the code word is fixed, allow representation of approximately n^2 numbers for n bits, rather than the n numbers of the…

Tokenization is a fundamental preprocessing step for almost all NLP tasks. In this paper, we propose efficient algorithms for the WordPiece tokenization used in BERT, from single-word tokenization to general text (e.g., sentence)…

Given a set $S$ of $n$ (distinct) keys from key space $[U]$, each associated with a value from $\Sigma$, the \emph{static dictionary} problem asks to preprocess these (key, value) pairs into a data structure, supporting value-retrieval…

Let $S$ be a string of length $n$ over an alphabet $\Sigma$ and let $Q$ be a subset of $\Sigma$ of size $q \geq 2$. The 'co-occurrence problem' is to construct a compact data structure that supports the following query: given an integer $w$…

Given a set $P$ of $n$ points in the plane and a multiset $W$ of $k$ weights with $k\leq n$, we assign each weight in $W$ to a distinct point in $P$ to minimize the maximum weighted distance from the weighted center of $P$ to any point in…

We introduce a new shared memory object: the write-and-f-array, provide its wait-free implementation and use it to construct an improved wait-free implementation of the fetch-and-add object. The write-and-f-array generalizes single-writer…

In the literature of algorithms, the specific computation model is often not explicit as it is assumed that the model of computation is the RAM (Random Access Machine) model. However, the RAM model itself is ill-founded in the literature,…