Related papers: A discrepancy lower bound for information complexi…
We present a technique of proving lower bounds for noisy computations. This is achieved by a theorem connecting computations on a kind of randomized decision trees and sampling based algorithms. This approach is surprisingly powerful, and…
The problem of distinguishing between a random function and a random permutation on a domain of size $N$ is important in theoretical cryptography, where the security of many primitives depend on the problem's hardness. We study the quantum…
We fully determine the communication complexity of approximating matrix rank, over any finite field $\mathbb{F}$. We study the most general version of this problem, where $0\leq r<R\leq n$ are given integers, Alice and Bob's inputs are…
We consider the problem of testing whether an unknown Boolean function $f$ is monotone versus $\epsilon$-far from every monotone function. The two main results of this paper are a new lower bound and a new algorithm for this well-studied…
This work studies information-computation gaps for statistical problems. A common approach for providing evidence of such gaps is to show sample complexity lower bounds (that are stronger than the information-theoretic optimum) against…
In this paper, we prove a strong XOR lemma for bounded-round two-player randomized communication. For a function $f:\mathcal{X}\times \mathcal{Y}\rightarrow\{0,1\}$, the $n$-fold XOR function $f^{\oplus n}:\mathcal{X}^n\times…
We give lower bounds on the communication complexity required to solve several computational problems in a distributed-memory parallel machine, namely standard matrix multiplication, stencil computations, comparison sorting, and the Fast…
Here we prove an asymptotically optimal lower bound on the information complexity of the k-party disjointness function with the unique intersection promise, an important special case of the well known disjointness problem, and the…
We introduce a two-parameter family of discrepancy measures, termed \emph{$(G,f)$-divergences}, obtained by applying a non-decreasing function $G$ to an $f$-divergence $D_f$. Building on Csisz\'ar's formulation of mutual $f$-information, we…
We prove $n^{1+\Omega(1/p)}/p^{O(1)}$ lower bounds for the space complexity of $p$-pass streaming algorithms solving the following problems on $n$-vertex graphs: * testing if an undirected graph has a perfect matching (this implies lower…
The polynomial method and the Ambainis's lower bound (or \emph{Alb}, for short) method are two main quantum lower bound techniques. While recently Ambainis showed that the polynomial method is not tight, the present paper aims at studying…
We show that any randomised Monte Carlo distributed algorithm for the Lov\'asz local lemma requires $\Omega(\log \log n)$ communication rounds, assuming that it finds a correct assignment with high probability. Our result holds even in the…
We investigate query-to-communication lifting theorems for models related to the quantum adversary bounds. Our results are as follows: 1. We show that the classical adversary bound lifts to a lower bound on randomized communication…
We show a tight lower bound of $\Omega(N \log\log N)$ on the number of transmissions required to compute the parity of $N$ input bits with constant error in a noisy communication network of $N$ randomly placed sensors, each having one input…
This paper introduces a bilateral matching mechanism to explain why different populations have different levels of cooperation. The traditional game theory assumes that individuals can acquire their neighbor's information without cost after…
We introduce a simple model illustrating the role of context in communication and the challenge posed by uncertainty of knowledge of context. We consider a variant of distributional communication complexity where Alice gets some information…
We provide a generic technique for constructing families of submodular functions to obtain lower bounds for submodular function minimization (SFM). Applying this technique, we prove that any deterministic SFM algorithm on a ground set of…
We study the maximum $k$-set coverage problem in the following distributed setting. A collection of sets $S_1,\ldots,S_m$ over a universe $[n]$ is partitioned across $p$ machines and the goal is to find $k$ sets whose union covers the most…
Information causality was proposed as a physical principle to put upper bound on the accessible information gain in a physical bi-partite communication scheme. Intuitively, the information gain cannot be larger than the amount of classical…
The distinguishability quantified by information measures after being processed by a private mechanism has been a useful tool in studying various statistical and operational tasks while ensuring privacy. To this end, standard…