Related papers: Optimal lower bounds for universal relation, and f…
From the output produced by a memoryless deletion channel from a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that…
We study the fundamental communication limits of information-theoretic secure aggregation in a hierarchical network consisting of a server, multiple relays, and multiple users per relay. Communication proceeds over two rounds and two hops,…
We consider the discrete memoryless symmetric primitive relay channel, where, a source $X$ wants to send information to a destination $Y$ with the help of a relay $Z$ and the relay can communicate to the destination via an error-free…
The celebrated result of Fischer, Lynch and Paterson is the fundamental lower bound for asynchronous fault tolerant computation: any 1-crash resilient asynchronous agreement protocol must have some (possibly measure zero) probability of not…
We consider the maximum weight $b$-matching problem in the random-order semi-streaming model. Assuming all weights are small integers drawn from $[1,W]$, we present a $2 - \frac{1}{2W} + \varepsilon$ approximation algorithm, using a memory…
We show tight lower bounds for the entire trade-off between space and query time for the Approximate Near Neighbor search problem. Our lower bounds hold in a restricted model of computation, which captures all hashing-based approaches. In…
Gap Hamming Distance is a well-studied problem in communication complexity, in which Alice and Bob have to decide whether the Hamming distance between their respective n-bit inputs is less than n/2-sqrt(n) or greater than n/2+sqrt(n). We…
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…
In this paper we study the two player randomized communication complexity of the sparse set disjointness and the exists-equal problems and give matching lower and upper bounds (up to constant factors) for any number of rounds for both of…
Communication is a major factor determining the performance of algorithms on current computing systems; it is therefore valuable to provide tight lower bounds on the communication complexity of computations. This paper presents a lower…
We study the problem of learning a most biased coin among a set of coins by tossing the coins adaptively. The goal is to minimize the number of tosses until we identify a coin i* whose posterior probability of being most biased is at least…
In 1981 Hong and Kung proved a lower bound on the amount of communication needed to perform dense, matrix-multiplication using the conventional $O(n^3)$ algorithm, where the input matrices were too large to fit in the small, fast memory. In…
In 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), the task is to list the $k$-error occurrences of $P$ in…
We introduce a new notion of information complexity for multi-pass streaming problems and use it to resolve several important questions in data streams. In the coin problem, one sees a stream of $n$ i.i.d. uniform bits and one would like to…
The two-way capacities of quantum channels determine the ultimate entanglement and secret-key distribution rates achievable by two distant parties that are connected by a noisy transmission line, in absence of quantum repeaters. Since…
The Collision problem is to decide whether a given list of numbers $(x_1,\ldots,x_n)\in[n]^n$ is $1$-to-$1$ or $2$-to-$1$ when promised one of them is the case. We show an $n^{\Omega(1)}$ randomised communication lower bound for the natural…
We investigate the sample-memory-pass trade-offs for pure exploration in multi-pass streaming multi-armed bandits (MABs) with the *a priori* knowledge of the optimality gap $\Delta_{[2]}$. Here, and throughout, the optimality gap…
The traditional requirement for a randomized streaming algorithm is just {\em one-shot}, i.e., algorithm should be correct (within the stated $\eps$-error bound) at the end of the stream. In this paper, we study the {\em tracking} problem,…
In this work, we establish lower-bounds against memory bounded algorithms for distinguishing between natural pairs of related distributions from samples that arrive in a streaming setting. In our first result, we show that any algorithm…
Round complexity is an extensively studied metric of distributed algorithms. In contrast, our knowledge of the \emph{message complexity} of distributed computing problems and its relationship (if any) with round complexity is still quite…