Related papers: Small Uncolored and Colored Choice Dictionaries

It is well known that n integers in the range [1,n^c] can be sorted in O(n) time in the RAM model using radix sorting. More generally, integers in any range [1,U] can be sorted in O(n sqrt{loglog n}) time. However, these algorithms use O(n)…

Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized…

Let $C_1,\dots,C_{d+1}\subset \mathbb{R}^d$ be $d+1$ point sets, each containing the origin in its convex hull. We call these sets color classes, and we call a sequence $p_1, \dots, p_{d+1}$ with $p_i \in C_i$, for $i = 1, \dots, d+1$, a…

We present a wait-free algorithm for proper coloring the n nodes of the asynchronous cycle $C_n$, where each crash-prone node starts with its (unique) identifier as input. The algorithm is independent of $n \geq 3$, and runs in…

Diverse selection statements -- if-then-else, switch and try-catch -- are commonly used in modern programming languages. To make things simple, we propose a unifying statement for selection. This statement is of the form seqor(G_1,...,G_n)…

We are considering RAMs $N_{n}$, with wordlength $n=2^{d}$, whose arithmetic instructions are the arithmetic operations multiplication and addition modulo $2^{n}$, the unary function $ \min\lbrace 2^{x}, 2^{n}-1\rbrace$, the binary…

Most of the attention in statistical compression is given to the space used by the compressed sequence, a problem completely solved with optimal prefix codes. However, in many applications, the storage space used to represent the prefix…

A rank-select index for a sequence $B=(b_1,\ldots,b_n)$ of $n$ bits is a data structure that, if provided with an operation to access $\Theta(\log n)$ arbitrary consecutive bits of $B$ in constant time (thus $B$ is stored outside of the…

We study a variant of online bin packing, called colorful bin packing. In this problem, items that are presented one by one are to be packed into bins of size 1. Each item i has a size s_i \in [0,1] and a color c_i \in C, where C is a set…

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…

In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms.…

Encoding data structures store enough information to answer the queries they are meant to support but not enough to recover their underlying datasets. In this paper we give the first encoding data structure for the challenging problem of…

Suppose we are asked to preprocess a string \(s [1..n]\) such that later, given a substring's endpoints, we can quickly count how many distinct characters it contains. In this paper we give a data structure for this problem that takes \(n…

Let $s$ be a string of length $n$ over an alphabet of constant size $\sigma$ and let $c$ and $\epsilon$ be constants with (1 \geq c \geq 0) and (\epsilon > 0). Using (O (n)) time, (O (n^c)) bits of memory and one pass we can always encode…

A Random Access query to a string $T\in [0..\sigma)^n$ asks for the character $T[i]$ at a given position $i\in [0..n)$. In $O(n\log\sigma)$ bits of space, this fundamental task admits constant-time queries. While this is optimal in the…

As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…

We consider encoding problems for range queries on arrays. In these problems the goal is to store a structure capable of recovering the answer to all queries that occupies the information theoretic minimum space possible, to within lower…

Suppose a language $L$ can be decided by a bounded-error randomized algorithm that runs in space $S$ and time $n \cdot \text{poly}(S)$. We give a randomized algorithm for $L$ that still runs in space $O(S)$ and time $n \cdot \text{poly}(S)$…

The circular dictionary matching problem is an extension of the classical dictionary matching problem where every string in the dictionary is interpreted as a circular string: after reading the last character of a string, we can move back…

Many techniques in computer vision, machine learning, and statistics rely on the fact that a signal of interest admits a sparse representation over some dictionary. Dictionaries are either available analytically, or can be learned from a…