Communication complexity

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

Simplified lower bounds on the multiparty communication complexity of disjointness

Abstract: We show that the deterministic number-on-forehead communication complexity of set disjointness for k parties on a universe of size n is Ω(n/ 4k). This gives the first lower bound that is linear in n, nearly matching Grolmusz's upper bound of O(log2(n) + k2n/2k). We also simplify the proof of Sherstov's [EQUATION] lower bound for the randomized communication complexity of set disjointness.

Multi-agent deployment for visibility coverage in polygonal environments with holes

Abstract: SUMMARY This article presents a distributed algorithm for a group of robotic agents with omnidirectional vision to deploy into nonconvex polygonal environments with holes. Agents begin deployment from a common point, possess no prior knowledge of the environment, and operate only under line-of-sight sensing and communication. The objective of the deployment is for the agents to achieve full visibility coverage of the environment while maintaining line-of-sight connectivity with each other. This is achieved by incrementally partitioning the environment into distinct regions, each c ompletely visible from some agent. Proofs are given of (i) convergence, (ii) upper bounds on the time and number of agents required, and (iii) bounds on the memory and communication complexity. Simulation results and description of robust extensions are also included. Copyright c 0000 John Wiley & Sons, Ltd.

Generalizations of the distributed Deutsch-Jozsa promise problem

Abstract: In the distributed Deutsch–Jozsa promise problem, two parties are to determine whether their respective strings x, y in {0,1} n are at the Hamming distance H(x, y) = 0 or H(x, y) = $\frac{n}{2}$. Buhrman et al. (STOC' 98) proved that the exact quantum communication complexity of this problem is O(log n) while the deterministic communication complexity is Omega(n). This was the first impressive (exponential) gap between quantum and classical communication complexity. In this paper, we generalize the above distributed Deutsch-Jozsa promise problem to determine, for any fixed $\frac{n}{2}$ <= k <= n, whether H(x, y) = 0 or H(x, y) = k, and show that an exponential gap between exact quantum and deterministic communication complexity still holds if k is an even such that $\frac{1}{2}$n <= k < (1 - lambda)n, where 0 < lambda < $\frac{1}{2}$ is given. We also deal with a promise version of the well-known disjointness problem and show also that for this promise problem there exists an exponential gap between quantum (and also probabilistic) communication complexity and deterministic communication complexity of the promise version of such a disjointness problem. Finally, some applications to quantum, probabilistic and deterministic finite automata of the results obtained are demonstrated.

Control Communication Complexity of Distributed Control Systems

Abstract: This paper introduces a measure of communication complexity for a two-agent distributed control system where controls are subject to finite bandwidth communication constraints. The proposed complexity measure is an extension of the idea of communication complexity defined in distributed computing. Applying this classical concept to control problems with finite communication constraints leads to a new perspective and a host of new questions, some of which are investigated in this paper. In particular, one can connect the proposed complexity with the traditional communication complexity via upper bound and lower bound inequalities. Moreover, the proposed complexity is shown to be intricately related to the dynamical characteristics of the underlying system.