相关论文: On-line algorithms for multiplication and division…
Let the base $\beta$ be a complex number, $|\beta|>1$, and let $A \subset \C$ be a finite alphabet of digits. The \emph{$A$-spectrum} of $\beta$ is the set $S_{A}(\beta) = \{\sum_{k=0}^n a_k\beta^k \mid n \in \mathbb{N}, \ a_k \in {A}\}$.…
We consider numeration systems where digits are integers and the base is an algebraic number $\beta$ such that $|\beta|>1$ and $\beta$ satisfies a polynomial where one coefficient is dominant in a certain sense. For this class of bases…
It is argued that transformation processes (generation rules) showing evidence of a long evolutionary history in universal computing systems can be generalized. The explicit function class $ \Omega $ is defined as follows: "Operators whose…
An on-line chain partitioning algorithm receives the points of the poset from some externally determined list. Being presented with a new point the algorithm learns the comparability status of this new point to all previously presented…
An on-line chain partitioning algorithm receives the elements of a poset one at a time, and when an element is received, irrevocably assigns it to one of the chains. In this paper, we present an on-line algorithm that partitions posets of…
We study parallel algorithms for addition of numbers having finite representation in a positional numeration system defined by a base $\beta$ in $\mathbb{C}$ and a finite digit set $\mathcal{A}$ of contiguous integers containing $0$. For a…
We consider positional numeration systems with negative real base $-\beta$, where $\beta>1$, and study the extremal representations in these systems, called here the greedy and lazy representations. We give algorithms for determination of…
We consider the reordering buffer problem on a line consisting of n equidistant points. We show that, for any constant delta, an (offline) algorithm that has a buffer (1-delta) k performs worse by a factor of Omega(log n) than an offline…
In this work a rationalized algorithm for calculating the quotient of two complex numbers is presented which reduces the number of underlying real multiplications. The performing of a complex number division using the naive method takes 4…
An algebraic number $\beta \in \mathbb{C}$ with no conjugate of modulus 1 can serve as the base of a numeration system $(\beta, \mathcal{A})$ with parallel addition, i.e., the sum of two operands represented in base $\beta$ with digits from…
Completing Loo-Keng Hua's approach to the real number system pioneered in 1962, this paper defines arithmetical operations directly on infinite decimals without appealing to any ordering structure. Therefore, the widespread belief that…
An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemer\'edi proved that any on-line algorithm could be forced to use…
We consider the following online optimization problem. We are given a graph $G$ and each vertex of the graph is assigned to one of $\ell$ servers, where servers have capacity $k$ and we assume that the graph has $\ell \cdot k$ vertices.…
Multiplication is indispensable and is one of the core operations in many modern applications including signal processing and neural networks. Conventional right-to-left (RL) multiplier extensively contributes to the power consumption, area…
The present paper proposes a new parallel algorithm for the modular division $u/v\bmod \beta^s$, where $u,\; v,\; \beta$ and $s$ are positive integers $(\beta\ge 2)$. The algorithm combines the classical add-and-shift multiplication scheme…
The multistep solving strategy consists in a divide-and-conquer approach: when a multivariate polynomial system is computationally infeasible to solve directly, one variable is assigned over the elements of the base finite field, and the…
We study the online sorting problem, where $n$ real numbers arrive in an online fashion, and the algorithm must immediately place each number into an array of size $(1+\varepsilon) n$ before seeing the next number. After all $n$ numbers are…
In \emph{Online Sorting}, an array of $n$ initially empty cells is given. At each time step $t$, an element $x_t \in [0,1]$ arrives and must be placed irrevocably into an empty cell without any knowledge of future arrivals. We aim to…
In \emph{Online Sorting}, an array of $n$ initially empty cells is given. At each time step $t$, an element $x_t \in [0,1]$ arrives and must be placed irrevocably into an empty cell without any knowledge of future arrivals. We aim to…
Online Analytical Processing (OLAP) comprises tools and algorithms that allow querying multidimensional databases. It is based on the multidimensional model, where data can be seen as a cube, where each cell contains one or more measures…