Communication complexity

About: Communication complexity is a research topic. Over the lifetime, 3870 publications have been published within this topic receiving 105832 citations.

Communication-Efficient Unconditional MPC with Guaranteed Output Delivery

Abstract: We study the communication complexity of unconditionally secure MPC with guaranteed output delivery over point-to-point channels for corruption threshold \(t < n/3\). We ask the question: “is it possible to construct MPC in this setting s.t. the communication complexity per multiplication gate is linear in the number of parties?” While a number of works have focused on reducing the communication complexity in this setting, the answer to the above question has remained elusive for over a decade.

An Approximation Algorithm for Approximation Rank

Abstract: One of the strongest techniques available for showing lower bounds on bounded-error 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 communication matrix. Krause showed that the logarithm of approximation rank is a lower bound in the randomized case, and later Buhrman and de Wolf showed it could also be used for quantum communication complexity. As a lower bound technique, approximation rank has two main drawbacks: it is difficult to compute, and it is not known to lower bound the model of quantum communication complexity with entanglement. We give a polynomial time constant factor approximation algorithm to the logarithm of approximation rank, and show that the logarithm of approximation rank is a lower bound on quantum communication complexity with entanglement.

The log-approximate-rank conjecture is false

Abstract: We construct a simple and total XOR function F on 2n variables that has only O(√n) spectral norm, O(n2) approximate rank and O(n2.5) approximate nonnegative rank. We show it has polynomially large randomized bounded-error communication complexity of Ω(√n). This yields the first exponential gap between the logarithm of the approximate rank and randomized communication complexity for total functions. Thus F witnesses a refutation of the Log-Approximate-Rank Conjecture (LARC) which was posed by Lee and Shraibman as a very natural analogue for randomized communication of the still unresolved Log-Rank Conjecture for deterministic communication. The best known previous gap for any total function between the two measures is a recent 4th-power separation by G'o'os, Jayram, Pitassi and Watson. Additionally, our function F refutes Grolmusz’s Conjecture and a variant of the Log-Approximate-Nonnegative-Rank Conjecture, suggested recently by Kol, Moran, Shpilka and Yehudayoff, both of which are implied by the LARC. The complement of F has exponentially large approximate nonnegative rank. This answers a question of Lee and Kol et al., showing that approximate nonnegative rank can be exponentially larger than approximate rank. The function F also falsifies a conjecture about parity measures of Boolean functions made by Tsang, Wong, Xie and Zhang. The latter conjecture implied the Log-Rank Conjecture for XOR functions. We are pleased to note that shortly after we published our results two independent groups of researchers, Anshu, Boddu and Touchette, and Sinha and de Wolf, used our function F to prove that the Quantum-Log-Rank Conjecture is also false by showing that F has Ω(n1/6) quantum communication complexity.

A Distributed Optimum Algorithm for Target Coverage in Wireless Sensor Networks

Abstract: In order to maximize the network lifetime for target coverage, we propose a distributed optimum coverage algorithm for point target in wireless sensor networks. In this paper, we first present a 1-hop local target coverage problem, next analyze the critical restraint of this problem and introduced the definition of key target, then designed an energy utility function, last established an adaptive adjustment mechanism of the waiting time. Measurement results show that the new algorithm extends 20% longer network lifetime, has good scalability and stability, and a lower computational and communication complexity.

Hadamard tensors and lower bounds on multiparty communication complexity

Abstract: We develop a new method for estimating the discrepancy of tensors associated with multiparty communication problems in the “Number on the Forehead” model of Chandra, Furst and Lipton. We define an analogue of the Hadamard property of matrices for tensors in multiple dimensions and show that any k-party communication problem represented by a Hadamard tensor must have Ω(n/2k) multiparty communication complexity. We also exhibit constructions of Hadamard tensors, giving Ω(n/2k) lower bounds on multiparty communication complexity for a new class of explicitly defined Boolean functions.