Related papers: On The Communication Complexity of Linear Algebrai…
In many problems, the inputs arrive over time, and must be dealt with irrevocably when they arrive. Such problems are online problems. A common method of solving online problems is to first solve the corresponding linear program, and then…
We study the multi-message broadcast problem using abstract MAC layer models of wireless networks. These models capture the key guarantees of existing MAC layers while abstracting away low-level details such as signal propagation and…
The topology-aware Massively Parallel Computation (MPC) model is proposed and studied recently, which enhances the classical MPC model by the awareness of network topology. The work of Hu et al. on topology-aware MPC model considers only…
We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…
One of the strongest techniques available for showing lower bounds on quantum communication complexity is the logarithm of the approximation rank of the communication matrix--the minimum rank of a matrix which is entrywise close to the…
We investigate the problem of approximating the product $a^TBc$, where $a,c\in S^{n-1}$ and $B\in O_n$, in models of communication complexity and streaming algorithms. The worst meaningful approximation is to simply decide whether the…
We describe new lower bounds for randomized communication complexity and query complexity which we call the partition bounds. They are expressed as the optimum value of linear programs. For communication complexity we show that the…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
In this paper we study the inherent trade-off between time and communication complexity for the distributed consensus problem. In our model, communication complexity is measured as the maximum data throughput (in bits per second) sent…
We introduce a framework for proving lower bounds on computational problems over distributions against algorithms that can be implemented using access to a statistical query oracle. For such algorithms, access to the input distribution is…
We consider the problem of resolving contention in communication networks with selfish users. In a \textit{contention game} each of $n \geq 2$ identical players has a single information packet that she wants to transmit using one of $k \geq…
In this paper, we study robust distributed sub-optimal coordination of linear agents subject to input nonlinearities. Inspired by the robust agreement literature, we formulate a bounded distributed sub-optimal coordination problem, in which…
In this paper, we exploit linear programming duality in the online setting (i.e., where input arrives on the fly) from the unique perspective of designing lower bounds on the competitive ratio. In particular, we provide a general technique…
Information theoretically secure multi-party computation (MPC) is a central primitive of modern cryptography. However, relatively little is known about the communication complexity of this primitive. In this work, we develop powerful…
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…
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 distributed sketching complexity of connectivity. In distributed graph sketching, an $n$-node graph $G$ is distributed to $n$ players such that each player sees the neighborhood of one vertex. The players then…
Content delivery networks often employ caching to reduce transmission rates from the central server to the end users. Recently, the technique of coded caching was introduced whereby coding in the caches and coded transmission signals from…
We study the one-way number-on-the-forehead (NOF) communication complexity of the $k$-layer pointer jumping problem with $n$ vertices per layer. This classic problem, which has connections to many aspects of complexity theory, has seen a…
Leadership games provide a powerful paradigm to model many real-world settings. Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for real-world…