Related papers: On The Communication Complexity of Linear Algebrai…
Coordinating a fully distributed multi-agent system (MAS) can be challenging when the communication channel has very limited capabilities in terms of sending rate and packet payload. When the MAS has to deal with active obstacles in a…
In this paper we address game theory problems arising in the context of network security. In traditional game theory problems, given a defender and an attacker, one searches for mixed strategies which minimize a linear payoff functional. In…
We study two basic graph parameters, the chromatic number and the orthogonal rank, in the context of classical and quantum exact communication complexity. In particular, we consider two types of communication problems that we call promise…
The Gap-Hamming-Distance problem arose in the context of proving space lower bounds for a number of key problems in the data stream model. In this problem, Alice and Bob have to decide whether the Hamming distance between their $n$-bit…
We study the multiparty communication complexity of high dimensional permutations, in the Number On the Forehead (NOF) model. This model is due to Chandra, Furst and Lipton (CFL) who also gave a nontrivial protocol for the Exactly-n problem…
The matrix chain problem consists in finding the parenthesization of a matrix product $M := A_1 A_2 \cdots A_n$ that minimizes the number of scalar operations. In practical applications, however, one frequently encounters more complicated…
We present efficient and practical algorithms for a large, distributed system of processors to achieve reliable computations in a secure manner. Specifically, we address the problem of computing a general function of several private inputs…
Reducing communication - either between levels of a memory hierarchy or between processors over a network - is a key component of performance optimization (in both time and energy) for many problems, including dense linear algebra, particle…
Artificial intelligence and robotic competitions are accompanied by a class of game paradigms in which each player privately commits a strategy to a game system which simulates the game using the collected joint strategy and then returns…
Brouwer's fixed point theorem states that any continuous function from a compact convex space to itself has a fixed point. Roughgarden and Weinstein (FOCS 2016) initiated the study of fixed point computation in the two-player communication…
We consider the point-to-point message passing model of communication in which there are $k$ processors with individual private inputs, each $n$-bit long. Each processor is located at the node of an underlying undirected graph and has…
The existence of a polynomial pivot rule for the simplex method for linear programming, policy iteration for Markov decision processes, and strategy improvement for parity games each are prominent open problems in their respective fields.…
In the communication problem $\mathbf{UR}$ (universal relation) [KRW95], Alice and Bob respectively receive $x, y \in\{0,1\}^n$ with the promise that $x\neq y$. The last player to receive a message must output an index $i$ such that…
In this paper, we study two variants of the online metric matching problem. The first problem is the online metric matching problem where all the servers are placed at one of two positions in the metric space. We show that a simple greedy…
This paper focuses on studying the message complexity of implicit leader election in synchronous distributed networks of diameter two. Kutten et al.\ [JACM 2015] showed a fundamental lower bound of $\Omega(m)$ ($m$ is the number of edges in…
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…
Within personalized marketing, a recommendation issue known as multicampaign assignment is to overcome a critical problem, known as the multiple recommendation problem which occurs when running several personalized campaigns simultaneously.…
In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…
We formalize AI alignment as a multi-objective optimization problem called $\langle M,N,\varepsilon,\delta\rangle$-agreement, in which a set of $N$ agents (including humans) must reach approximate ($\varepsilon$) agreement across $M$…
We study the one-way two-party communication complexity of Maximum Matching in the semi-robust setting where the edges of a maximum matching are randomly partitioned between Alice and Bob, but all remaining edges of the input graph are…