Related papers: Communication Lower Bounds via Critical Block Sens…
We resolve several fundamental questions in the area of distributed functional monitoring, initiated by Cormode, Muthukrishnan, and Yi (SODA, 2008). In this model there are $k$ sites each tracking their input and communicating with a…
We prove lower bounds for the direct sum problem for two-party bounded error randomised multiple-round communication protocols. Our proofs use the notion of information cost of a protocol, as defined by Chakrabarti, Shi, Wirth and Yao and…
We investigate the randomized and quantum communication complexities of the well-studied Equality function with small error probability $\epsilon$, getting optimal constant factors in the leading terms in a number of different models. In…
We show new lower bounds in the \emph{Merlin-Arthur} (MA) communication model and the related \emph{annotated streaming} or stream verification model. The MA communication model is an enhancement of the classical communication model, where…
We study the problem of simultaneous search for multiple targets over a multidimensional unit cube and derive fundamental resolution limits of non-adaptive querying procedures using the 20 questions estimation framework. The performance…
In secure multiparty computation (MPC), mutually distrusting users collaborate to compute a function of their private data without revealing any additional information about their data to other users. While it is known that information…
We study space-bounded communication complexity for unitary implementation in distributed quantum processors, where we restrict the number of qubits per processor to ensure practical relevance and technical non-triviality. We model…
Results from the communication complexity literature have demonstrated that stable matching requires communication: one cannot find or verify a stable match without having access to essentially all of the ordinal preference information held…
Sensitivity, block sensitivity and certificate complexity are basic complexity measures of Boolean functions. The famous sensitivity conjecture claims that sensitivity is polynomially related to block sensitivity. However, it has been…
We give the first super-polynomial separation in the power of bounded-depth boolean formulas vs. circuits. Specifically, we consider the problem Distance $k(n)$ Connectivity, which asks whether two specified nodes in a graph of size $n$ are…
We study the problem of identifying correlations in multivariate data, under information constraints: Either on the amount of memory that can be used by the algorithm, or the amount of communication when the data is distributed across…
The approximate degree of a Boolean function is the minimum degree of real polynomial that approximates it pointwise. For any Boolean function, its approximate degree serves as a lower bound on its quantum query complexity, and generically…
The classic lower bound of Kuhn, Moscibroda and Wattenhofer [JACM 2016] states that approximate maximum matching and approximate vertex cover (among other problems) in the LOCAL model require $\Omega(\min\{\sqrt{\frac{\log n}{\log\log n}},…
Sorting is a fundamental problem in computer science. In the classical setting, it is well-known that $(1\pm o(1)) n\log_2 n$ comparisons are both necessary and sufficient to sort a list of $n$ elements. In this paper, we study the Noisy…
Communication compression is an essential strategy for alleviating communication overhead by reducing the volume of information exchanged between computing nodes in large-scale distributed stochastic optimization. Although numerous…
At each iteration of a Block Coordinate Descent method one minimizes an approximation of the objective function with respect to a generally small set of variables subject to constraints in which these variables are involved. The…
Theoreticians have studied distributed algorithms in the radio network model for close to three decades. A significant fraction of this work focuses on lower bounds for basic communication problems such as wake-up (symmetry breaking among…
Robust sunflowers are a generalization of combinatorial sunflowers that have applications in monotone circuit complexity, DNF sparsification, randomness extractors, and recent advances on the Erd\H{o}s-Rado sunflower conjecture. The recent…
In this paper, we develop a new communication model to prove a data structure lower bound for the dynamic interval union problem. The problem is to maintain a multiset of intervals $\mathcal{I}$ over $[0, n]$ with integer coordinates,…
Multiplication is one of the most fundamental computational problems, yet its true complexity remains elusive. The best known upper bound, by F\"{u}rer, shows that two $n$-bit numbers can be multiplied via a boolean circuit of size $O(n \lg…