Communication complexity

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

Exploiting communication complexity for multilevel logic synthesis

Abstract: A multilevel logic synthesis technique based on minimizing communication complexity is presented. This approach is believed to be viable because, for many types of circuits, the area needed is dominated by interconnections. By minimizing communication complexity and interconnect, area is reduced. This approach performs especially well for functions that are hierarchically decomposable (e.g., adders, parity generators, comparators, etc.). Unlike many other multilevel logic synthesis techniques, a lower bound can be computed to determine how well the synthesis was performed. A new multilevel logic synthesis program based on the techniques described for reducing communication complexity is presented. >

A Hierarchical Methodology for Word-Length Optimization of Signal Processing Systems

Abstract: The problem of converting floating point algorithms to implementation friendly fixed point formats is often solved as an optimization problem where the precision is traded to gain in the implementation cost. The complexity of the problem is known to grow exponentially with more optimizable variables. This paper proposes a divide and conquer technique to solve the growing size of the problem. The approach in this technique is original in the sense that it is formulated from a designers perspective rather than merely attempting to divide and conquer at the algorithmic level. This paper introduces the single noise source model based on which the proposed technique is built. A mixed approach for error propagation is also explained keeping in view of the elements in the circuit that cannot be handled analytically.

Contention Resolution in a Non-synchronized Multiple Access Channel

Abstract: Multiple access channel is a well-known communication model that deploys properties of many network systems, such as Aloha multi-access systems, local area Ethernet networks, satellite communication systems, packet radio networks. The fundamental aspect of this model is to provide efficient communication and computation in the presence of restricted access to the communication resource: at most one station can successfully transmit at a time, and a wasted round occurs when more than one station attempts to transmit at the same time. In this work we consider the problem of contention resolution in a multiple access channel in a realistic scenario when up to k stations out of n join the channel at different times. The goal is to let at least one station to transmit alone, which results in successful delivery of the message through the channel. We present three deterministic algorithms: two of them working under some constrained scenarios, and achieving asymptotically optimal time complexity Θ(k log(n/k)), while the third general algorithm accomplishes the goal in time O(k logn log log n).

Secure linear algebra using linearly recurrent sequences

Abstract: In this work we present secure two-party protocols for various core problems in linear algebra. Our main result is a protocol to obliviously decide singularity of an encrypted matrix: Bob holds an n×n matrix, encrypted with Alice's secret key, and wants to learn whether or not the matrix is singular (while leaking nothing further). We give an interactive protocol between Alice and Bob that solves the above problem in O(log n) communication rounds and with overall communication complexity of roughly O(n2) (note that the input size is n2). Our techniques exploit certain nice mathematical properties of linearly recurrent sequences and their relation to the minimal and characteristic polynomial of the input matrix, following [Wiedemann, 1986]. With our new techniques we are able to improve the round complexity of the communication efficient solution of [Nissim and Weinreb, 2006] from O(n0.275) to O(log n). At the core of our results we use a protocol that securely computes the minimal polynomial of an encrypted matrix. Based on this protocol we exploit certain algebraic reductions to further extend our results to the problems of securely computing rank and determinant, and to solving systems of linear equations (again with low round and communication complexity).

On the average communication complexity of asynchronous distributed algorithms

Abstract: We study the communication complexity of asynchronous distributed algorithms. Such algorithms can generate excessively many messages in the worst case. Nevertheless, we show that, under certain probabilistic assumptions, the expected number of messages generated per time unit is bounded by a polynomial function of the number of processors under a very general model of distributed computation. Furthermore, for constant-degree processor graphs, the expected number of generated messages is only O(nT), where n is the number of processors and T is the running time. We conclude that (under our model) any asynchronous algorithm with good time complexity will also have good communication complexity, on the average.