Related papers: Two Source Extractors for Asymptotically Optimal E…

A general method of coding over expansion is proposed,which allows one to reduce the highly non-trivial problems of coding over analog channels and compressing analog sources to a set of much simpler subproblems, coding over discrete…

Monotone operator theory and fixed point theory for nonexpansive mappings are central areas in modern nonlinear analysis and optimization. Although these areas are fairly well developed, almost all examples published are based on…

Min-entropy sampling gives a bound on the min-entropy of a randomly chosen subset of a string, given a bound on the min-entropy of the whole string. K\"onig and Renner showed a min-entropy sampling theorem that holds relative to quantum…

We consider the $0$-Extension problem, where we are given an undirected graph $\mathcal{G}=(V,E)$ equipped with non-negative edge weights $w:E\rightarrow \mathbb{R}^+$, a collection $ T=\{ t_1,\ldots,t_k\}\subseteq V$ of $k$ special…

We give the first O(m polylog(n)) time algorithms for approximating maximum flows in undirected graphs and constructing polylog(n) -quality cut-approximating hierarchical tree decompositions. Our algorithm invokes existing algorithms for…

We prove several new results for seedless condensers in the context of three related classes of sources: Non-Oblivious Symbol Fixing (NOSF) sources, online NOSF (oNOSF) sources [AORSV, EUROCRYPT'20], and adversarial Chor-Goldreich (aCG)…

Spectral hypergraph sparsification, an attempt to extend well-known spectral graph sparsification to hypergraphs, has been extensively studied over the past few years. For undirected hypergraphs, Kapralov, Krauthgamer, Tardos, and…

In classical and quantum information theory, operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to store given data are normally characterized by one of two…

The study of regenerating codes has advanced tremendously in recent years. However, most known constructions require large field size, and hence may be hard to implement in practice. By using notions from the theory of extension fields, we…

We study the problem of extracting randomness from somewhere-random sources, and related combinatorial phenomena: partition analogues of Shearer's lemma on projections. A somewhere-random source is a tuple $(X_1, \ldots, X_t)$ of (possibly…

Given a graph with a source vertex $s$, the Single Source Replacement Paths (SSRP) problem is to compute, for every vertex $t$ and edge $e$, the length $d(s,t,e)$ of a shortest path from $s$ to $t$ that avoids $e$. A Single-Source Distance…

This paper proposes to develop a new variant of the two-time-scale stochastic approximation to find the roots of two coupled nonlinear operators, assuming only noisy samples of these operators can be observed. Our key idea is to leverage…

We introduce a new computational model for data streams: asymptotically exact streaming algorithms. These algorithms have an approximation ratio that tends to one as the length of the stream goes to infinity while the memory used by the…

In a recent breakthrough, Chen, Hirahara and Ren prove that $\mathsf{S_2E}/_1 \not\subset \mathsf{SIZE}[2^n/n]$ by giving a single-valued $\mathsf{FS_2P}$ algorithm for the Range Avoidance Problem ($\mathsf{Avoid}$) that works for…

We present an algorithm for the maximum matching problem in dynamic (insertion-deletions) streams with *asymptotically optimal* space complexity: for any $n$-vertex graph, our algorithm with high probability outputs an $\alpha$-approximate…

This paper is concerned with the asymptotic optimality of spectral coarse spaces for two-level iterative methods. Spectral coarse spaces, namely coarse spaces obtained as the span of the slowest modes of the used one-level smoother, are…

The problem of secure multiterminal source coding with side information at the eavesdropper is investigated. This scenario consists of a main encoder (referred to as Alice) that wishes to compress a single source but simultaneously…

Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…

Let $s$ denote a distinguished source vertex of a non-negatively real weighted and undirected graph $G$ with $n$ vertices and $m$ edges. In this paper we present two efficient \emph{single-source approximate-distance sensitivity oracles},…

Let $G =<S>$ be a solvable permutation group of the symmetric group $S_n$ given as input by the generating set $S$. We give a deterministic polynomial-time algorithm that computes an \emph{expanding generating set} of size $\tilde{O}(n^2)$…