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An initializable array is an array that supports the read and write operations for any element and the initialization of the entire array. This paper proposes a simple in-place algorithm to implement an initializable array of length $N$…

We solve the dynamic Predecessor Problem with high probability (whp) in constant time, using only $n^{1+\delta}$ bits of memory, for any constant $\delta > 0$. The input keys are random wrt a wider class of the well studied and practically…

We show that for all given $n,t,w \in \{1,2,...\}$ with $n<2^w$, an array of $n$ entries of $w$ bits each can be represented on a word RAM with a word length of $w$ bits in at most $nw+\lceil n(t/(2 w))^t\rceil$ bits of uninitialized memory…

A \emph{resizable array} is an array that can \emph{grow} and \emph{shrink} by the addition or removal of items from its end, or both its ends, while still supporting constant-time \emph{access} to each item stored in the array given its…

We extend the Faulty RAM model by Finocchi and Italiano (2008) by adding a safe memory of arbitrary size $S$, and we then derive tradeoffs between the performance of resilient algorithmic techniques and the size of the safe memory. Let…

A choice dictionary is a data structure that can be initialized with a parameter $n\in\{1,2,\ldots\}$ and subsequently maintains an initially empty subset $S$ of $\{1,\ldots,n\}$ under insertion, deletion, membership queries and an…

The task of accumulating a portion of a list of values, whose values may be updated at any time, is widely used throughout various applications in computer science. While it is trivial to accomplish this task without any constraints,…

In this paper we consider the problem of encoding data into \textit{repeat-free} sequences in which sequences are imposed to contain any $k$-tuple at most once (for predefined $k$). First, the capacity of the repeat-free constraint are…

We consider the task of assigning unique integers to a group of processes in an asynchronous distributed system of a total of $n$ processes prone to crashes that communicate through shared read-write registers. In the Renaming problem, an…

We present a data structure that stores a sequence $s[1..n]$ over alphabet $[1..\sigma]$ in $n\Ho(s) + o(n)(\Ho(s){+}1)$ bits, where $\Ho(s)$ is the zero-order entropy of $s$. This structure supports the queries \access, \rank\ and \select,…

The rank problem in succinct data structures asks to preprocess an array A[1..n] of bits into a data structure using as close to n bits as possible, and answer queries of the form rank(k) = Sum_{i=1}^k A[i]. The problem has been intensely…

A robust positioning pattern is a large array that allows a mobile device to locate its position by reading a possibly corrupted small window around it. In this paper, we provide constructions of binary positioning patterns, equipped with…

We study the effects of finite-precision representation of source's probabilities on the efficiency of classic source coding algorithms, such as Shannon, Gilbert-Moore, or arithmetic codes. In particular, we establish the following simple…

The choice dictionary is introduced as a data structure that can be initialized with a parameter $n\in\mathbb{N}=\{1,2,\ldots\}$ and subsequently maintains an initially empty subset $S$ of $\{1,\ldots,n\}$ under insertion, deletion,…

A new array based data structure named black-white array (BWA) is introduced as an effective and efficient alternative to the list or tree based data structures for dynamic data set. It consists of two sub-arrays, one white and one black of…

We consider the problem of designing low-redundancy codes in settings where one must correct deletions in conjunction with substitutions or adjacent transpositions; a combination of errors that is usually observed in DNA-based data storage.…

In the static retrieval problem, a data structure must answer retrieval queries mapping a set of $n$ keys in a universe $[U]$ to $v$-bit values. Information-theoretically, retrieval data structures can use as little as $nv$ bits of space.…

We assume the permutation $\pi$ is given by an $n$-element array in which the $i$-th element denotes the value $\pi(i)$. Constructing its inverse in-place (i.e. using $O(\log{n})$ bits of additional memory) can be achieved in linear time…

Assuming we are in a Word-RAM model with word size $w$, we show that we can construct in $o(w)$ time an error correcting code with a constant relative positive distance that maps numbers of $w$ bits into $\Theta(w)$-bit numbers, and such…

Dictionaries have been one of the central questions in data structures. A dictionary data structure maintains a set of key-value pairs under insertions and deletions such that given a query key, the data structure efficiently returns its…