Communication complexity

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

Multiparty Communication Complexity and Threshold Circuit Size of AC^0

Abstract: We prove an n^Omega(1)/4^k lower bound on the randomized k-party communication complexity of depth 4 AC^0 functions in the number-on-forehead (NOF) model for up to Theta(log n) players. These are the first non-trivial lower bounds for general NOF multiparty communication complexity for any AC^0 function for omega(log log n) players. For non-constant k the bounds are larger than all previous lower bounds for any AC^0 function even for simultaneous communication complexity. Our lower bounds imply the first super polynomial lower bounds for the simulation of AC^0 by MAJ-SYMM-AND circuits, showing that the well-known quasipolynomial simulations of AC^0 by such circuits are qualitatively optimal, even for formulas of small constant depth. We also exhibit a depth 5 formula in NPc-BPPc for up to Theta(log n) players and derive an Omega(2^{sqrt{log n}/sqrt{k}}) lower bound on the randomized k-party NOF communication complexity of set disjointness for up to Theta(log^{1/3} n) players which is significantly larger than the O(log log n) players allowed in the best previous lower bounds for multiparty set disjointness. We prove other strong results for depth 3 and 4 AC^0 functions.

Elections in anonymous networks

Abstract: We address the problem of electing a leader in an anonymous, asynchronous network of arbitrary topology Our algorithms are considerably simpler than known algorithms and have equal or improved communication complexity

The round complexity of distributed sorting: extended abstract

Abstract: We consider the model of fully connected networks, where in each round each node can send an O(log n)-bit message to each other node (this is the CONGEST model with diameter 1). It is known that in this model, min-weight spanning trees can be found in O(log log n) rounds. In this paper we show that distributed sorting, where each node has at most n items, can be done in time O(log log n) as well. It is also shown that selection can be done in O(1) time. (Using a concurrent result by Lenzen and Wattenhofer, the complexity of sorting is further reduced to constant.) Our algorithms are randomized, and the stated complexity bounds hold with high probability.

Communication locality in secure multi-party computation: how to run sublinear algorithms in a distributed setting

Abstract: We devise multi-party computation protocols for general secure function evaluation with the property that each party is only required to communicate with a small number of dynamically chosen parties. More explicitly, starting with n parties connected via a complete and synchronous network, our protocol requires each party to send messages to (and process messages from) at most polylog(n) other parties using polylog(n) rounds. It achieves secure computation of any polynomial-time computable randomized function f under cryptographic assumptions, and tolerates up to $({1\over 3} - \epsilon) \cdot n$ statically scheduled Byzantine faults. We then focus on the particularly interesting setting in which the function to be computed is a sublinear algorithm: An evaluation of f depends on the inputs of at most q=o(n) of the parties, where the identity of these parties can be chosen randomly and possibly adaptively. Typically, q=polylog(n). While the sublinear query complexity of f makes it possible in principle to dramatically reduce the communication complexity of our general protocol, the challenge is to achieve this while maintaining security: in particular, while keeping the identities of the selected inputs completely hidden. We solve this challenge, and we provide a protocol for securely computing such sublinear f that runs in polylog(n)+O(q) rounds, has each party communicating with at most q ·polylog(n) other parties, and supports message sizespolylog(n) ·(l+n), where l is the parties' input size. Our optimized protocols rely on a multi-signature scheme, fully homomorphic encryption (FHE), and simulation-sound adaptive NIZK arguments. However, we remark that multi-signatures and FHE are used to obtain our bounds on message size and round complexity. Assuming only standard digital signatures and public-key encryption, one can still obtain the property that each party only communicates with polylog(n) other parties. We emphasize that the scheduling of faults can depend on the initial PKI setup of digital signatures and the NIZK parameters.

Frequency Domain Decision Feedback Equalization for Uplink SC-FDMA

Abstract: Single carrier frequency division multiple access (SC-FDMA) is one well-known scheme, which has recently become a preferred choice for uplink channels. Due to the usage of single carrier, the performance of SC-FDMA systems degrades in deep frequency selective fading channels. In this paper, we propose a structure of equalizer based on frequency domain decision feedback which could be used for multi-user SC-FDMA systems. Specific parameters of the equalizer are analyzed as well. This algorithm is applicable to various carrier allocations in multi-user systems such as localized allocation, distributed allocation, and frequency-hopping (FH) allocation. To reduce the complexity, it is not necessary to derive the inversion of matrix, which is required in the traditional decision feedback equalizer for single carrier frequency domain equalization (SC-FDE-DFE). It is shown by the simulation results that perfect performance could be achieved under all kinds of situations for multi-user systems. This structure can be used in the broadcasting uplink channels with SC-FDMA scheme.