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In this paper we present two efficient methods for reconstructing a rational number from several residue-modulus pairs, some of which may be incorrect. One method is a natural generalization of that presented by Wang, Guy and Davenport in cite{WGD1982} (for reconstructing a rational number from textit{correct} modular images), and also of an algorithm presented in cite{Abb1991} for reconstructing an textit{integer} value from several residue-modulus pairs, some of which may be incorrect.
Let $b ge 2$ and $ell ge 1$ be integers. We establish that there is an absolute real number $K$ such that all the partial quotients of the rational number $$ prod_{h = 0}^ell , (1 - b^{-2^h}), $$ of denominator $b^{2^{ell+1} - 1}$, do not exceed $exp(K (log b)^2 sqrt{ell} 2^{ell/2})$.
For a nonincreasing function $psi$, let $textrm{Exact}(psi)$ be the set of complex numbers that are approximable by complex rational numbers to order $psi$ but to no better order. In this paper, we obtain the Hausdorff dimension and packing dimension
In this work, we initiate the study of fault tolerant Max Cut, where given an edge-weighted undirected graph $G=(V,E)$, the goal is to find a cut $Ssubseteq V$ that maximizes the total weight of edges that cross $S$ even after an adversary removes $k
A $k$-spanner of a graph $G$ is a sparse subgraph that preserves its shortest path distances up to a multiplicative stretch factor of $k$, and a $k$-emulator is similar but not required to be a subgraph of $G$. A classic theorem by Thorup and Zwick [
It is now widely accepted that the CMOS technology implementing irreversible logic will hit a scaling limit beyond 2016, and that the increased power dissipation is a major limiting factor. Reversible computing can potentially require arbitrarily sma