Related papers: A lower bound for bounded round quantum communicat…
Data dissemination is a fundamental task in distributed computing. This paper studies broadcast problems in various innovative models where the communication network connecting $n$ processes is dynamic (e.g., due to mobility or failures)…
The $CONGEST$ model for distributed network computing is well suited for analyzing the impact of limiting the throughput of a network on its capacity to solve tasks efficiently. For many "global" problems there exists a lower bound of…
Computing set joins of two inputs is a common task in database theory. Recently, Van Gucht, Williams, Woodruff and Zhang [PODS 2015] considered the complexity of such problems in the natural model of (classical) two-party communication…
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of…
We show a new duality between the polynomial margin complexity of $f$ and the discrepancy of the function $f \circ \textsf{XOR}$, called an $\textsf{XOR}$ function. Using this duality, we develop polynomial based techniques for…
The approximate degree of a Boolean function $f\colon\{0,1\}^n\to\{0,1\}$ is the minimum degree of a real polynomial $p$ that approximates $f$ pointwise: $|f(x)-p(x)|\leq1/3$ for all $x\in\{0,1\}^n.$ For every $\delta>0,$ we construct CNF…
Quantum communication typically involves a linear chain of repeater stations, each capable of reliable local quantum computation and connected to their nearest neighbors by unreliable communication links. The communication rate in existing…
In their seminal paper from 2004, Kuhn, Moscibroda, and Wattenhofer (KMW) proved a hardness result for several fundamental graph problems in the LOCAL model: For any (randomized) algorithm, there are input graphs with $n$ nodes and maximum…
We prove that there is a trade-off relation between the entanglement cost and the number of rounds of communication, for two distant parties to accomplish a bidirectional quantum information task by local operations and classical…
We prove lower bounds for the direct sum problem for two-party bounded error randomised multiple-round communication protocols. Our proofs use the notion of information cost of a protocol, as defined by Chakrabarti, Shi, Wirth and Yao and…
The nearest lattice point problem in $\mathbb{R}^n$ is formulated in a distributed network with $n$ nodes. The objective is to minimize the probability that an incorrect lattice point is found, subject to a constraint on inter-node…
The problem of detecting network structures plays a central role in distributed computing. One of the fundamental problems studied in this area is to determine whether for a given graph $H$, the input network contains a subgraph isomorphic…
The problem of distinguishing between a random function and a random permutation on a domain of size $N$ is important in theoretical cryptography, where the security of many primitives depend on the problem's hardness. We study the quantum…
In standard number-in-hand multi-party communication complexity, performance is measured as the total number of bits transmitted globally in the network. In this paper, we study a variation called local communication complexity in which…
There is a close relationship between the communication complexity and information complexity of communication problems, as demonstrated by results such as Shannon's noiseless source coding theorem, and the Slepian-Wolf theorem. Here, we…
We prove that the fidelity of two exemplary communication complexity protocols, allowing for an N-1 bit communication, can be exponentially improved by N-1 (unentangled) qubit communication. Taking into account, for a fair comparison, all…
We present a linear program for the one-way version of the partition bound (denoted $\mathsf{prt}^1_\varepsilon(f)$). We show that it characterizes one-way randomized communication complexity $\mathsf{R}_\varepsilon^1(f)$ with shared…
We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique…
We prove three new lower bounds for graph connectivity in the $1$-bit broadcast congested clique model, BCC$(1)$. First, in the KT-$0$ version of BCC$(1)$, in which nodes are aware of neighbors only through port numbers, we show an…
Consider a face F in an arrangement of n Jordan curves in the plane, no two of which intersect more than s times. We prove that the combinatorial complexity of F is O(\lambda_s(n)), O(\lambda_{s+1}(n)), and O(\lambda_{s+2}(n)), when the…