Related papers: Gadgetless Lifting Beats Round Elimination: Improv…
In this paper, we derive a new dimension-free non-asymptotic upper bound for the quadratic $k$-means excess risk related to the quantization of an i.i.d sample in a separable Hilbert space. We improve the bound of order $\mathcal{O} \bigl(…
In the past few years, a successful line of research has lead to lower bounds for several fundamental local graph problems in the distributed setting. These results were obtained via a technique called round elimination. On a high level,…
Population protocols are a fundamental model in distributed computing, where many nodes with bounded memory and computational power have random pairwise interactions over time. This model has been studied in a rich body of literature aiming…
The best known solutions for $k$-message broadcast in dynamic networks of size $n$ require $\Omega(nk)$ rounds. In this paper, we see if these bounds can be improved by smoothed analysis. We study perhaps the most natural randomized…
We use critical block sensitivity, a new complexity measure introduced by Huynh and Nordstr\"om (STOC 2012), to study the communication complexity of search problems. To begin, we give a simple new proof of the following central result of…
We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…
We develop a new upper bound on the capacity of the relay channel that is tighter than previously known upper bounds. This upper bound is proved using traditional weak converse techniques involving mutual information inequalities and…
We show that randomization can lead to significant improvements for a few fundamental problems in distributed tracking. Our basis is the {\em count-tracking} problem, where there are $k$ players, each holding a counter $n_i$ that gets…
We give improved separations for the query complexity analogue of the log-approximate-rank conjecture i.e. we show that there are a plethora of total Boolean functions on $n$ input bits, each of which has approximate Fourier sparsity at…
The decades-old Pattern Matching with Edits problem, given a length-$n$ string $T$ (the text), a length-$m$ string $P$ (the pattern), and a positive integer $k$ (the threshold), asks to list all fragments of $T$ that are at edit distance at…
In this paper, we give a conditional lower bound of $n^{\Omega(k)}$ on running time for the classic k-median and k-means clustering objectives (where n is the size of the input), even in low-dimensional Euclidean space of dimension four,…
We develop lower bounds on communication in the memory hierarchy or between processors for nested bilinear algorithms, such as Strassen's algorithm for matrix multiplication. We build on a previous framework that establishes communication…
We continue the study of the communication complexity of gap cycle counting problems. These problems have been introduced by Verbin and Yu [SODA 2011] and have found numerous applications in proving streaming lower bounds. In the noisy gap…
In this paper we obtain some bounds on communication complexity of Gap Hamming Distance problem ($\mathsf{GHD}^n_{L, U}$): Alice and Bob are given binary string of length $n$ and they are guaranteed that Hamming distance between their…
Inspired by the great success of machine learning in the past decade, people have been thinking about the possibility of improving the theoretical results by exploring data distribution. In this paper, we revisit a fundamental problem…
We study the tradeoff between the statistical error and communication cost of distributed statistical estimation problems in high dimensions. In the distributed sparse Gaussian mean estimation problem, each of the $m$ machines receives $n$…
The process of state preparation, its transmission and subsequent measurement can be classically simulated through the communication of some amount of classical information. Recently, we proved that the minimal communication cost is the…
We consider the task of minimizing the sum of smooth and strongly convex functions stored in a decentralized manner across the nodes of a communication network whose links are allowed to change in time. We solve two fundamental problems for…
The current best approximation algorithms for $k$-median rely on first obtaining a structured fractional solution known as a bi-point solution, and then rounding it to an integer solution. We improve this second step by unifying and…
Surpassing the repeaterless bound is a crucial task on the way towards realizing long-distance quantum key distribution. In this paper, we focus on the protocol proposed by Azuma et al. in [Nature Communications 6, 10171 (2015)], which can…