Communication complexity

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

Communication-Optimal Distributed Clustering

Abstract: Clustering large datasets is a fundamental problem with a number of applications in machine learning. Data is often collected on different sites and clustering needs to be performed in a distributed manner with low communication. We would like the quality of the clustering in the distributed setting to match that in the centralized setting for which all the data resides on a single site. In this work, we study both graph and geometric clustering problems in two distributed models: (1) a point-to-point model, and (2) a model with a broadcast channel. We give protocols in both models which we show are nearly optimal by proving almost matching communication lower bounds. Our work highlights the surprising power of a broadcast channel for clustering problems; roughly speaking, to spectrally cluster $n$ points or $n$ vertices in a graph distributed across $s$ servers, for a worst-case partitioning the communication complexity in a point-to-point model is $n \cdot s$, while in the broadcast model it is $n + s$. A similar phenomenon holds for the geometric setting as well. We implement our algorithms and demonstrate this phenomenon on real life datasets, showing that our algorithms are also very efficient in practice.

Communication Complexity and Secure Function Evaluation.

Abstract: We suggest two new methodologies for the design of efficient secure protocols, that differ with respect to their underlying computational models. In one methodology we utilize the communication complexity tree (or branching for f and transform it into a secure protocol. In other words, "any function f that can be computed using communication complexity c can be can be computed securely using communication complexity that is polynomial in c and a security parameter". The second methodology uses the circuit computing f, enhanced with look-up tables as its underlying computational model. It is possible to simulate any RAM machine in this model with polylogarithmic blowup. Hence it is possible to start with a computation of f on a RAM machine and transform it into a secure protocol. We show many applications of these new methodologies resulting in protocols efficient either in communication or in computation. In particular, we exemplify a protocol for the "millionaires problem", where two participants want to compare their values but reveal no other information. Our protocol is more efficient than previously known ones in either communication or computation.

Efficient Privacy-Preserving Facial Expression Classification

Abstract: This paper proposes an efficient algorithm to perform privacy-preserving (PP) facial expression classification (FEC) in the client-server model. The server holds a database and offers the classification service to the clients. The client uses the service to classify the facial expression (FaE) of subject. It should be noted that the client and server are mutually untrusted parties and they want to perform the classification without revealing their inputs to each other. In contrast to the existing works, which rely on computationally expensive cryptographic operations, this paper proposes a lightweight algorithm based on the randomization technique. The proposed algorithm is validated using the widely used JAFFE and MUG FaE databases. Experimental results demonstrate that the proposed algorithm does not degrade the performance compared to existing works. However, it preserves the privacy of inputs while improving the computational complexity by $120$ times and communication complexity by $31$ percent against the existing homomorphic cryptography based approach.

Tight Lower Bounds for Multi-pass Stream Computation Via Pass Elimination

Abstract: There is a natural relationship between lower bounds in the multi-pass stream model and lower bounds in multi-round communication. However, this connection is less understood than the connection between single-pass stream computation and one-way communication. In this paper, we consider data-stream problems for which reductions from natural multi-round communication problems do not yield tight bounds or do not apply. While lower bounds are known for some of these data-stream problems, many of these only apply to deterministic or comparison-based algorithms, whereas the lower bounds we present apply to any (possibly randomized) algorithms. Our results are particularly relevant to evaluating functions that are dependent on the ordering of the stream, such as the longest increasing subsequence and a variant of tree pointer jumping in which pointers are revealed according to a post-order traversal. Our approach is based on establishing "pass-elimination" type results that are analogous to the round-elimination results of Miltersen et al. [23] and Sen [29]. We demonstrate our approach by proving tight bounds for a range of data-stream problems including finding the longest increasing sequences (a problem that has recently become very popular [22,16,30,15,12] and we resolve an open question of [30]), constructing convex hulls and fixed-dimensional linear programming (generalizing results of [8] to randomized algorithms), and the "greater-than" problem (improving results of [9]). These results will also clarify one of the main messages of our work: sometimes it is necessary to prove lower bounds directly for stream computation rather than proving a lower bound for a communication problem and then constructing a reduction to a data-stream problem.

The distributed k-server problem-a competitive distributed translator for k-server algorithms

Abstract: The authors consider the k-server problem in a distributed setting. Given a network of n processors, and k identical mobile servers, requests for service appear at the processors and a server must reach the request point. Besides modeling problems in computer networks where k identical mobile resources are shared by the processors of the network, this models a realistic situation where the transfer of information is costly and there is no central control that governs the behavior of servers that move around to satisfy requests for service. The problem is that of devising algorithms that minimize not only the travel of the server but also the communication cost incurred for the transmission of control messages. The main contribution is a general translator to transform any deterministic global-control competitive k-server algorithm into a distributed competitive one. As consequences they get poly(k)-competitive distributed algorithms for the line, trees and the ring. >