Communication complexity

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

Communication complexity of document exchange

Abstract: We have two users, A and B, who hold documents x and y respectively. Neither of the users has any information about the other''s document. They exchange messages so that B computes x; it may be required that A compute y as well. Our goal is to design communication protocols with the main objective of minimizing the total number of bits they exchange; other objectives are minimizing the number of rounds and the complexity of internal computations. An important notion which determines the efficiency of the protocols is how one measures the distance between x and y. We consider several metrics for measuring this distance, namely the Hamming metric, the Levenshtein metric (edit distance), and a new LZ metric, which is introduced in this paper. We show how to estimate the distance between x and y using a single message of logarithmic size. For each metric, we present the first communication-efficient protocols, which often match the corresponding lower bounds. A consequence of these are error-correcting codes for these error models which correct up to d errors in n characters using O(d log n) bits. Our most interesting methods use a new histogram transformation that we introduce to convert edit distance to L1 distance.

Communication on noisy channels: a coding theorem for computation

Abstract: Communication is critical to distributed computing, parallel computing, or any situation in which automata interact-hence its significance as a resource in computation. In view of the likelihood of errors occurring in a lengthy interaction, it is desirable to incorporate this possibility in the model of communication. The author relates the noisy channel and the standard (noise less channel) complexities of a communication problem by establishing a 'two-way' or interactive analogue of Shanon's coding theorem: every noiseless channel protocol can be simulated by a private-coin noisy channel protocol whose time bound is proportional to the original (noiseless) time bound and inversely proportional to the capacity of the channel, while the protocol errs with vanishing probability. The method involves simulating the original protocol while implementing a hierarchical system of progress checks which ensure that errors of any magnitude in the simulation are, with high probability, rapidly eliminated. >

The Arrow Distributed Directory Protocol

Abstract: Most practical techniques for locating remote objects in a distributed system suffer from problems of scalability and locality of reference We have devised the Arrow distributed directory protocol, a scalable and local mechanism for ensuring mutually exclusive access to mobile objects This directory has communication complexity optimal within a factor of (1+MST-stretch(G))/2, where MST-stretch(G) is the “minimum spanning tree stretch” of the underlying network

The Communication Complexity of Correlation

Abstract: We examine the communication required for generating random variables remotely. One party Alice is given a distribution D, and she has to send a message to Bob, who is then required to generate a value with distribution exactly D. Alice and Bob are allowed to share random bits generated without the knowledge of D. There are two settings based on how the distribution D provided to Alice is chosen. If D is itself chosen randomly from some set (the set and distribution are known in advance) and we wish to minimize the expected communication in order for Alice to generate a value y, with distribution D, then we characterize the communication required in terms of the mutual information between the input to Alice and the output Bob is required to generate. If D is chosen from a set of distributions D, and we wish to devise a protocol so that the expected communication (the randomness comes from the shared random string and Alice's coin tosses) is small for each D isin D, then we characterize the communication required in this case in terms of the channel capacity associated with the set D. Our proofs are based on an improved rejection sampling procedure that relates the relative entropy between two distributions to the communication complexity of generating one distribution from the other. As an application of these results, we derive a direct sum theorem in communication complexity that substantially improves the previous such result shown by Jain et al. (2003).

Lattices, mobius functions and communications complexity

Abstract: A general framework for the study of a broad class of communication problems is developed. It is based on a recent analysis of the communication complexity of graph connectivity. The approach makes use of combinatorial lattice theory. >