相关论文: The effective entropy of next/previous larger/smal…

`Twenty questions' is a guessing game played by two players: Bob thinks of an integer between $1$ and $n$, and Alice's goal is to recover it using a minimal number of Yes/No questions. Shannon's entropy has a natural interpretation in this…

In the problem of minimal perfect hashing, we are given a size $k$ subset $\mathcal{A}$ of a universe of keys $[n] = \{1,2, \cdots, n\}$, for which we wish to construct a hash function $h: [n] \to [k]$ such that $h(\cdot)$ maps…

We give an implementation of an algorithm that uses fair coin flips to simulate fair rolls of an $n$-sided die. A register plays the role of an entropy pool and holds entropy that is generated as a by-product during each die roll and that…

There is a common problem of operating on hash values of elements of some database. In this paper there will be analyzed informational content of such general task and how to practically approach such found lower boundaries. Minimal prefix…

Although many authors have considered how many ternary comparisons it takes to sort a multiset $S$ of size $n$, the best known upper and lower bounds still differ by a term linear in $n$. In this paper we restrict our attention to online…

Consider the set of all sequences of $n$ outcomes, each taking one of $m$ values, that satisfy a number of linear constraints. If $m$ is fixed while $n$ increases, most sequences that satisfy the constraints result in frequency vectors…

We resolve the space complexity of single-pass streaming algorithms for approximating the classic set cover problem. For finding an $\alpha$-approximate set cover (for any $\alpha= o(\sqrt{n})$) using a single-pass streaming algorithm, we…

The ever-growing size of neural networks poses serious challenges on resource-constrained devices, such as embedded sensors. Compression algorithms that reduce their size can mitigate these problems, provided that model performance stays…

We consider in this paper the problem of computing the entropy of a braid. We recall its definition and construct, for each braid, a sequence of real numbers, whose limit is its entropy. We state one conjecture about the convergence speed,…

In this paper, we look into the adaptive bitprobe model that stores subsets of size at most four from a universe of size m, and answers membership queries using two bitprobes. We propose a scheme that stores arbitrary subsets of size four…

In quantum Shannon theory, various kinds of quantum entropies are used to characterize the capacities of noisy physical systems. Among them, min-entropy and its smooth version attract wide interest especially in the field of quantum…

Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…

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…

Optimization results are one method for understanding neural computation from Nature's perspective and for defining the physical limits on neuron-like engineering. Earlier work looks at individual properties or performance criteria and…

Deriving formulations for computing and estimating tight worst-case size increases for conjunctive queries with various constraints has been at the core of theoretical database research. If the problem has no constraints or only one…

When algorithms for sorting and searching are applied to keys that are represented as bit strings, we can quantify the performance of the algorithms not only in terms of the number of key comparisons required by the algorithms but also in…

Noise causes severe difficulties in implementing quantum computing and quantum cryptography. Several schemes have been suggested to reduce this problem, mainly focusing on quantum computation. Motivated by quantum cryptography, we suggest a…

We study the problem of $2$-dimensional orthogonal range counting with additive error. Given a set $P$ of $n$ points drawn from an $n\times n$ grid and an error parameter $\eps$, the goal is to build a data structure, such that for any…

In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal…

For a given partition of (1, 2, ..., 2n) into two disjoint subsets A and B with n elements in each, consider the maximum number of times any integer occurs as the difference between an element of A and an element of B. The minimum value of…