Related papers: The Pattern Matrix Method (Journal Version)
The decades-old Pattern Matching with Edits problem, given a length-$n$ string $T$ (the text), a length-$m$ string $P$ (the pattern), and a positive integer $k$ (the threshold), asks to list all fragments of $T$ that are at edit distance at…
We give a tight lower bound of Omega(\sqrt{n}) for the randomized one-way communication complexity of the Boolean Hidden Matching Problem [BJK04]. Since there is a quantum one-way communication complexity protocol of O(\log n) qubits for…
Consider the "Number in Hand" multiparty communication complexity model, where k players holding inputs x_1,...,x_k in {0,1}^n communicate to compute the value f(x_1,...,x_k) of a function f known to all of them. The main lower bound…
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…
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…
The communication class $\mathbf{UPP}^{\text{cc}}$ is a communication analog of the Turing Machine complexity class $\mathbf{PP}$. It is characterized by a matrix-analytic complexity measure called sign-rank (also called dimension…
In the tradition of Gabor's 1946 landmark paper [1], we advocate a time-frequency (TF) approach to communications. TF methods for communications have been proposed very early (see the box History). While several tutorial papers and book…
We obtain a lower bound of n^Omega(1) on the k-party randomized communication complexity of the Disjointness function in the `Number on the Forehead' model of multiparty communication when k is a constant. For k=o(loglog n), the bounds…
We prove new bounds on the quantum communication complexity of the disjointness and equality problems. For the case of exact and non-deterministic protocols we show that these complexities are all equal to n+1, the previous best lower bound…
We show several results related to interactive proof modes of communication complexity. First we show lower bounds for the QMA-communication complexity of the functions Inner Product and Disjointness. We describe a general method to prove…
We introduce a new fundamental algorithm called Matrix-POAFD to solve the matrix least square problem. The method is based on the matching pursuit principle. The method directly extracts, among the given features as column vectors of the…
Broadcast protocols enable a set of $n$ parties to agree on the input of a designated sender, even facing attacks by malicious parties. In the honest-majority setting, randomization and cryptography were harnessed to achieve…
The polynomial method from circuit complexity has been applied to several fundamental problems and obtains the state-of-the-art running times. As observed in [Alman and Williams, STOC 2017], almost all applications of the polynomial method…
We introduce new models and new information theoretic measures for the study of communication complexity in the natural peer-to-peer, multi-party, number-in-hand setting. We prove a number of properties of our new models and measures, and…
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…
We use the venerable "fooling set" method to prove new lower bounds on the quantum communication complexity of various functions. Let f:X x Y-->{0,1} be a Boolean function, fool^1(f) its maximal fooling set size among 1-inputs, Q_1^*(f) its…
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,…
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…
We explore multi-round quantum memoryless communication protocols. These are restricted version of multi-round quantum communication protocols. The "memoryless" term means that players forget history from previous rounds, and their behavior…
This paper is motivated by the problem of error control in network coding when errors are introduced in a random fashion (rather than chosen by an adversary). An additive-multiplicative matrix channel is considered as a model for random…