Related papers: Direct Sum Theorems From Fortification
We show how to efficiently simulate the sending of a message M to a receiver who has partial information about the message, so that the expected number of bits communicated in the simulation is close to the amount of additional information…
We investigate the power of the most important lower bound technique in randomized communication complexity, which is based on an evaluation of the maximal size of approximately monochromatic rectangles, minimized over all distributions on…
Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known "entanglement…
We consider an instance of the following problem: Parties P_1,..., P_k each receive an input x_i, and a coordinator (distinct from each of these parties) wishes to compute f(x_1,..., x_k) for some predicate f. We are interested in one-round…
Information-theoretic methods have proven to be a very powerful tool in communication complexity, in particular giving an elegant proof of the linear lower bound for the two-party disjointness function, and tight lower bounds on…
We prove a lower bound on the communication complexity of computing the $n$-fold xor of an arbitrary function $f$, in terms of the communication complexity and rank of $f$. We prove that $D(f^{\oplus n}) \geq n \cdot…
We give a strong direct sum theorem for computing $xor \circ g$. Specifically, we show that for every function g and every $k\geq 2$, the randomized query complexity of computing the xor of k instances of g satisfies…
The focus of this paper is on {\em quantum distributed} computation, where we investigate whether quantum communication can help in {\em speeding up} distributed network algorithms. Our main result is that for certain fundamental network…
The problem Defensive $\delta$-Covering, for some covering range $\delta > 0$, is a continuous facility location problem on undirected graphs where all edges have unit length. It is a generalization of Defensive Dominating Set and…
The classical problem in network coding theory considers communication over multicast networks. Multiple transmitters send independent messages to multiple receivers which decode the same set of messages. In this work, computation over…
The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan. At the end of the first section I examine tree-balancing. In the second section I summarize the…
The Subset Sum problem asks whether a given set of $n$ positive integers contains a subset of elements that sum up to a given target $t$. It is an outstanding open question whether the $O^*(2^{n/2})$-time algorithm for Subset Sum by…
Three decades of research in communication complexity have led to the invention of a number of techniques to lower bound randomized communication complexity. The majority of these techniques involve properties of large submatrices…
We give a direct product theorem for the entanglement-assisted interactive quantum communication complexity of an $l$-player predicate $\mathsf{V}$. In particular we show that for a distribution $p$ that is product across the input sets of…
Linear computations over quantum many-to-one communication networks offer opportunities for communication cost improvements through schemes that exploit quantum entanglement among transmitters to achieve superdense coding gains, combined…
As statistical analyses become more central to science, industry and society, there is a growing need to ensure correctness of their results. Approximate correctness can be verified by replicating the entire analysis, but can we verify…
Given n positive integers, the Modular Subset Sum problem asks if a subset adds up to a given target t modulo a given integer m. This is a natural generalization of the Subset Sum problem (where m=+\infty) with ties to additive…
We consider the communication complexity of a number of distributed optimization problems. We start with the problem of solving a linear system. Suppose there is a coordinator together with $s$ servers $P_1, \ldots, P_s$, the $i$-th of…
We call $F:\{0, 1\}^n\times \{0, 1\}^n\to\{0, 1\}$ a symmetric XOR function if for a function $S:\{0, 1, ..., n\}\to\{0, 1\}$, $F(x, y)=S(|x\oplus y|)$, for any $x, y\in\{0, 1\}^n$, where $|x\oplus y|$ is the Hamming weight of the bit-wise…
We suggest two new methodologies for the design of efficient secure protocols, that differ with respect to their underlying computational models. In one methodology we utilize the communication complexity tree (or branching for f and…