相关论文: Computing the Ball Size of Frequency Permutations …

The computation of the elastic registration of two simple curves in higher dimensions and therefore of the elastic shape distance between them has been investigated by Srivastava et al. Assuming the first curve has one or more starting…

We propose a new $(1+O(\varepsilon))$-approximation algorithm with $O(n+ 1/\varepsilon^{\frac{(d-1)}{2}})$ running time for computing the diameter of a set of $n$ points in the $d$-dimensional Euclidean space for a fixed dimension $d$,…

Due to quantum fluctuations, non-orthogonal quantum states cannot be distinguished with complete certainty, making their underlying physical parameters difficult to resolve. Traditionally, it has been believed that the linewidth of a system…

Given a matrix $A \in \mathbb{R}^{m\times d}$ with singular values $\sigma_1\geq \cdots \geq \sigma_d$, and a random matrix $G \in \mathbb{R}^{m\times d}$ with iid $N(0,T)$ entries for some $T>0$, we derive new bounds on the Frobenius…

We survey permutation-based methods for approximate k-nearest neighbor search. In these methods, every data point is represented by a ranked list of pivots sorted by the distance to this point. Such ranked lists are called permutations. The…

The Gilbert-Varshamov bound (non-constructively) establishes the existence of binary codes of distance $1/2 -\epsilon$ and rate $\Omega(\epsilon^2)$ (where an upper bound of $O(\epsilon^2\log(1/\epsilon))$ is known). Ta-Shma [STOC 2017]…

In this paper, we study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+\varepsilon)$-approximation algorithm with $O(n+ 1/\varepsilon^{d-1})$…

A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of…

We consider linear error correcting codes associated to higher dimensional projective varieties defined over a finite field. The problem of determining the basic parameters of such codes often leads to some interesting and difficult…

This paper studies sets of matrices induced by quadratic inequalities. In particular, the center and radius of a smallest ball containing the set, called a Chebyshev center and the Chebyshev radius, are studied. In addition, this work…

It has been suggested that space-time might undergo fluctuations because of its intrinsic quantum nature. These fluctuations would pose a fundamental limit to the ability of measuring distances with arbitrary precision, beyond any…

In this paper we present a simple framework to study various distance problems of permutations, including the transposition and block-interchange distance of permutations as well as the reversal distance of signed permutations. These…

We propose an approximation method for thresholding of singular values using Chebyshev polynomial approximation (CPA). Many signal processing problems require iterative application of singular value decomposition (SVD) for minimizing the…

In classical coding theory, error-correcting codes are designed to protect against errors occurring at individual symbol positions in a codeword. However, in practical storage and communication systems, errors often affect multiple adjacent…

We prove an optimal $\Omega(n)$ lower bound on the randomized communication complexity of the much-studied Gap-Hamming-Distance problem. As a consequence, we obtain essentially optimal multi-pass space lower bounds in the data stream model…

Given four congruent balls $A, B, C, D$ in $R^{d}$ that have disjoint interior and admit a line that intersects them in the order $ABCD$, we show that the distance between the centers of consecutive balls is smaller than the distance…

Consider a geometric range space $(X,\c{A})$ where each data point $x \in X$ has two or more values (say $r(x)$ and $b(x)$). Also consider a function $\Phi(A)$ defined on any subset $A \in (X,\c{A})$ on the sum of values in that range e.g.,…

The sequence reconstruction problem asks for the recovery of a sequence from multiple noisy copies, where each copy may contain up to $r$ errors. In the case of permutations on \(n\) letters under the Hamming metric, this problem is closely…

We consider the problem of estimating the distance between two bodies of volume $\varepsilon$ located inside a $n$-dimensional ball $U$ of unit volume for $n\to\infty$. Let $A$ be a closed set with a smooth boundary of the volume…

This paper considers the quantization problem on the Grassmann manifold \mathcal{G}_{n,p}, the set of all p-dimensional planes (through the origin) in the n-dimensional Euclidean space. The chief result is a closed-form formula for the…