Related papers: Optimal Communication Complexity of Chained Index

We consider the situation in which a transmitter attempts to communicate reliably over a discrete memoryless channel while simultaneously ensuring covertness (low probability of detection) with respect to a warden, who observes the signals…

In this paper we explore fundamental problems in randomized communication complexity such as computing Set Intersection on sets of size $k$ and Equality Testing between vectors of length $k$. Sa\u{g}lam and Tardos and Brody et al. showed…

We study common randomness generation problems where $n$ players aim to generate same sequences of random coin flips where some subsets of the players share an independent common coin which can be tossed multiple times, and there is a…

The gossip problem (telephone problem) is an information dissemination problem in which each of $n$ nodes of a communication network has a unique piece of information that must be transmitted to all the other nodes using two-way…

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 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…

It was recently observed in [1], that in index coding, learning the coding matrix used by the server can pose privacy concerns: curious clients can extract information about the requests and side information of other clients. One approach…

The following question arises naturally in the study of graph streaming algorithms: "Is there any graph problem which is "not too hard", in that it can be solved efficiently with total communication (nearly) linear in the number $n$ of…

This paper makes three main contributions to the theory of communication complexity and stream computation. First, we present new bounds on the information complexity of AUGMENTED-INDEX. In contrast to analogous results for INDEX by Jain,…

We present new lower bounds that show that a polynomial number of passes are necessary for solving some fundamental graph problems in the streaming model of computation. For instance, we show that any streaming algorithm that finds a…

Consider the following gap cycle counting problem in the streaming model: The edges of a $2$-regular $n$-vertex graph $G$ are arriving one-by-one in a stream and we are promised that $G$ is a disjoint union of either $k$-cycles or…

We prove an optimal $\Omega(n)$ lower bound on the randomized communication complexity of the much-studied Gap-Hamming-Distance problem. As a consequence, we obtain essentially optimal multi-pass space lower bounds in the data stream model…

This paper considers the problem of covert communication with mismatched decoding, in which a sender wishes to reliably communicate with a receiver whose decoder is fixed and possibly sub-optimal, and simultaneously to ensure that the…

Mastermind is famous two-players game. The first player (codemaker) chooses a secret code which the second player (codebreaker) is supposed to crack within a minimum number of code guesses (queries). Therefore, codemaker's duty is to help…

We show that disjointness requires randomized communication Omega(n^{1/(k+1)}/2^{2^k}) in the general k-party number-on-the-forehead model of complexity. The previous best lower bound for k >= 3 was log(n)/(k-1). Our results give a…

A central question in information theory is to determine the maximum success probability that can be achieved in sending a fixed number of messages over a noisy channel. This was first studied in the pioneering work of Shannon who…

We focus on the following instance of an index coding problem, where a set of receivers are required to decode multiple messages, whilst each knows one of the messages a priori. In particular, here we consider a generalized setting where…

Since the 1960s Mastermind has been studied for the combinatorial and information theoretical interest the game has to offer. Many results have been discovered starting with Erd\H{o}s and R\'enyi determining the optimal number of queries…

We revisit the classic broadcast problem, wherein we have $k$ messages, each composed of $O(\log{n})$ bits, distributed arbitrarily across a network. The objective is to broadcast these messages to all nodes in the network. In the…

In the distributed triangle detection problem, we have an $n$-vertex network $G=(V,E)$ with one player for each vertex of the graph who sees the edges incident on the vertex. The players communicate in synchronous rounds using the edges of…