Communication complexity

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

Privacy preserving decision tree learning over multiple parties

Abstract: Data mining over multiple data sources has emerged as an important practical problem with applications in different areas such as data streams, data-warehouses, and bioinformatics. Although the data sources are willing to run data mining algorithms in these cases, they do not want to reveal any extra information about their data to other sources due to legal or competition concerns. One possible solution to this problem is to use cryptographic methods. However, the computation and communication complexity of such solutions render them impractical when a large number of data sources are involved. In this paper, we consider a scenario where multiple data sources are willing to run data mining algorithms over the union of their data as long as each data source is guaranteed that its information that does not pertain to another data source will not be revealed. We focus on the classification problem in particular and present an efficient algorithm for building a decision tree over an arbitrary number of distributed sources in a privacy preserving manner using the ID3 algorithm.

Cost-sensitive analysis of communication protocols

Abstract: : This paper introduces the notion of cost-sensitive communication complexity and exemplifies it on the following basic communication problems: computing a global function, network synchronization, clock synchronization, controlling protocols' worst-case execution, connected components, spanning tree, etc., constructing a minimum spanning tree, constructing a shortest path tree. (Author)

Secure multiparty computation of approximations

Abstract: Approximation algorithms can sometimes provide efficient solutions when no efficient exact computation is known. In particular, approximations are often useful in a distributed setting where the inputs are held by different parties and may be extremely large. Furthermore, for some applications, the parties want to compute a function of their inputs securely without revealing more information than necessary. In this work, we study the question of simultaneously addressing the above efficiency and security concerns via what we call secure approximations.We start by extending standard definitions of secure (exact) computation to the setting of secure approximations. Our definitions guarantee that no additional information is revealed by the approximation beyond what follows from the output of the function being approximated. We then study the complexity of specific secure approximation problems. In particular, we obtain a sublinear-communication protocol for securely approximating the Hamming distance and a polynomial-time protocol for securely approximating the permanent and related nP-hard problems.

AIDE: Fast and Communication Efficient Distributed Optimization

Abstract: In this paper, we present two new communication-efficient methods for distributed minimization of an average of functions. The first algorithm is an inexact variant of the DANE algorithm that allows any local algorithm to return an approximate solution to a local subproblem. We show that such a strategy does not affect the theoretical guarantees of DANE significantly. In fact, our approach can be viewed as a robustification strategy since the method is substantially better behaved than DANE on data partition arising in practice. It is well known that DANE algorithm does not match the communication complexity lower bounds. To bridge this gap, we propose an accelerated variant of the first method, called AIDE, that not only matches the communication lower bounds but can also be implemented using a purely first-order oracle. Our empirical results show that AIDE is superior to other communication efficient algorithms in settings that naturally arise in machine learning applications.

Single-peaked consistency and its complexity

Abstract: A common way of dealing with the paradoxes of preference aggregation consists in restricting the domain of admissible preferences. The most well-known such restriction is single-peakedness. In this paper we focus on the problem of determining whether a given profile is single-peaked with respect to some axis, and on the computation of such an axis. This problem has already been considered in [2]; we give here a more efficient algorithm and address some related issues, such as the number of orders that may be compatible with a given profile, or the communication complexity of preference aggregation under the single-peakedness assumption.