Related papers: A note on the partition bound for one-way classica…
In probability theory, the partition function is a factor used to reduce any probability function to a density function with total probability of one. Among other statistical models used to represent joint distribution, Markov random fields…
This work addresses two problems in the context of two-party communication complexity of functions. First, it concludes the line of research, which can be viewed as demonstrating qualitative advantage of quantum communication in the three…
The communication cost of algorithms (also known as I/O-complexity) is shown to be closely related to the expansion properties of the corresponding computation graphs. We demonstrate this on Strassen's and other fast matrix multiplication…
We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression,…
We consider the problem of distributed computation of the nearest lattice point for a two dimensional lattice. An interactive model of communication is considered. We address the problem of reconfiguring a specific rectangular partition, a…
We define a new model of quantum learning that we call Predictive Quantum (PQ). This is a quantum analogue of PAC, where during the testing phase the student is only required to answer a polynomial number of testing queries. We demonstrate…
This paper shows the strong converse and the dispersion of memoryless channels with cost constraints and performs refined analysis of the third order term in the asymptotic expansion of the maximum achievable channel coding rate, showing…
This paper presents a saddlepoint approximation of the random-coding union bound of Polyanskiy et al. for i.i.d. random coding over discrete memoryless channels. The approximation is single-letter, and can thus be computed efficiently.…
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…
Romashchenko and Zimand~\cite{rom-zim:c:mutualinfo} have shown that if we partition the set of pairs $(x,y)$ of $n$-bit strings into combinatorial rectangles, then $I(x:y) \geq I(x:y \mid t(x,y)) - O(\log n)$, where $I$ denotes mutual…
The paper presents fault-tolerant (FT) labeling schemes for general graphs, as well as, improved FT routing schemes. For a given $n$-vertex graph $G$ and a bound $f$ on the number of faults, an $f$-FT connectivity labeling scheme is a…
We derive several efficiently computable converse bounds for quantum communication over quantum channels in both the one-shot and asymptotic regime. First, we derive one-shot semidefinite programming (SDP) converse bounds on the amount of…
We explore several new converse bounds for classical communication over quantum channels in both the one-shot and asymptotic regimes. First, we show that the Matthews-Wehner meta-converse bound for entanglement-assisted classical…
The class $FORMULA[s] \circ \mathcal{G}$ consists of Boolean functions computable by size-$s$ de Morgan formulas whose leaves are any Boolean functions from a class $\mathcal{G}$. We give lower bounds and (SAT, Learning, and PRG) algorithms…
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…
Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only…
A major open problem in communication complexity is whether or not quantum protocols can be exponentially more efficient than classical protocols on _total_ Boolean functions in the two-party interactive model. The answer appears to be…
The process of state preparation, its transmission and subsequent measurement can be classically simulated through the communication of some amount of classical information. Recently, we proved that the minimal communication cost is the…
In this paper, we show a direct product theorm in the model of two-party bounded-round public-coin randomized communication complexity. For a relation f subset of X times Y times Z (X,Y,Z are finite sets), let R^{(t), pub}_e (f) denote the…
We study the query complexity of computing a function f:{0,1}^n-->R_+ in expectation. This requires the algorithm on input x to output a nonnegative random variable whose expectation equals f(x), using as few queries to the input x as…