We study the computational problem of determining covering radius a rational polytope. This parameter is defined as minimal dilation factor that needed for lattice translates correspondingly dilated polytope to cover whole space. As our main result, we describe new algorithm this problem, which simpler, more efficient and easier implement than only prior Kannan (1992). Motivated by variant famo...

The purpose of this paper is to introduce the class (a,b,c)-modified enriched Kannan pair mappings (T,S) in setting Banach space that includes mappings, contraction and nonexpansive some other mappings. Some examples are presented support concepts introduced herein. We establish existence common fixed point such pair. also show problem studied herein well posed. A convergence theorem for Krasno...

Let A be a 0/1 matrix of size m × n, and let p be the density of A (i.e., the number of ones divided by m · n). We show that A can be approximated in the cut norm within ε ·mnp by a sum of cut matrices (of rank 1), where the number of summands is independent of the sizem ·n of A, provided that A satisfies a certain boundedness condition. This decomposition can be computed in polynomial time. Th...

p ≥2 -cyclic and contractive self-mappings on a set of subsets of a metric space which are simultaneously accretive on the wholemetric space are investigated. The joint fulfilment of the p-cyclic contractiveness and accretive properties is formulated as well as potential relationships with cyclic self-mappings in order to be Kannan self-mappings. The existence and uniqueness of best proximity p...

We describe an FPGA accelerator for the Kannan–Fincke– Pohst enumeration algorithm (KFP) solving the Shortest Lattice Vector Problem (SVP). This is the first FPGA implementation of KFP specifically targeting cryptographically relevant dimensions. In order to optimize this implementation, we theoretically and experimentally study several facets of KFP, including its efficient parallelization and...

Vol. XLII (May 2005), 233–239 233 *Shibo Li is Assistant Professor of Marketing, Rutgers Business School—Newark and New Brunswick, Rutgers University (e-mail: [email protected]). Baohong Sun is Associate Professor of Marketing, Tepper School of Business, Carnegie Mellon University (e-mail: [email protected]). Ronald T. Wilcox is Associate Professor of Business Administration, Darde...

We provide a deterministic algorithm that finds, in $\epsilon^{-O(1)} n^2$ time, an $\epsilon$-regular Frieze-Kannan partition of a graph on $n$ vertices. The algorithm outputs an approximation of a given graph as a weighted sum of $\epsilon^{-O(1)}$ many complete bipartite graphs. As a corollary, we give a deterministic algorithm for estimating the number of copies of $H$ in an $n$-vertex grap...

We developed the operators ideal in this article by extending s -soft reals and a particular space of sequences with soft real numbers. The criteria necessary for Nakano sequence numbers given definite function to be prequasi Banach closed are investigated. This space’s ( id="M2"> R ) normal structural features ...