Communication complexity

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

LIMITS and Applications of Group Algebras for Parameterized Problems

Abstract: The fastest known randomized algorithms for several parameterized problems use reductions to the k-MlD problem: detection of multilinear monomials of degree k in polynomials presented as circuits The fastest known algorithm for k-MlD is based on 2k evaluations of the circuit over a suitable algebra We use communication complexity to show that it is essentially optimal within this evaluation framework On the positive side, we give additional applications of the method: finding a copy of a given tree on k nodes, a minimum set of nodes that dominate at least t nodes, and an m-dimensional k-matching In each case, we achieve a faster algorithm than what was known before We also apply the algebraic method to problems in exact counting Among other results, we show that a variation of it can break the trivial upper bounds for the disjoint summation problem

Performance evaluation of trellis-coded modulation schemes

Abstract: A description of the algorithms to evaluate the main parameters determining the performance of a trellis-coded modulation (TCM) scheme is presented. TCM schemes are divided into classes that have an increasing degree of symmetry, so as to properly match the various algorithms to each class. The algorithms are compared in terms of computational complexity and tested on a set of multidimensional PSK codes. >

From information to exact communication

Abstract: We develop a new local characterization of the zero-error information complexity function for two-party communication problems, and use it to compute the exact internal and external information complexity of the 2-bit AND function: IC(AND,0) = C∧≅ 1.4923 bits, and ICext(AND,0) = log2 3 ≅ 1.5839 bits. This leads to a tight (upper and lower bound) characterization of the communication complexity of the set intersection problem on subsets of {1,...,n} (the player are required to compute the intersection of their sets), whose randomized communication complexity tends to C∧⋅ n pm o(n) as the error tends to zero.The information-optimal protocol we present has an infinite number of rounds. We show this is necessary by proving that the rate of convergence of the r-round information cost of AND to IC(AND,0)=C∧ behaves like Θ(1/r2), i.e. that the r-round information complexity of AND is C∧+Θ(1/r2).We leverage the tight analysis obtained for the information complexity of AND to calculate and prove the exact communication complexity of the set disjointness function Disjn(X,Y) = - vi=1n AND(xi,yi) with error tending to 0, which turns out to be = CDISJ⋅ n pm o(n), where CDISJ≅ 0.4827. Our rate of convergence results imply that an asymptotically optimal protocol for set disjointness will have to use ω(1) rounds of communication, since every r-round protocol will be sub-optimal by at least Ω(n/r2) bits of communication.We also obtain the tight bound of 2/ln2 k pm o(k) on the communication complexity of disjointness of sets of size ≤ k. An asymptotic bound of Θ(k) was previously shown by Hastad and Wigderson.

Propagation and Leader Election in a Multihop Broadcast Environment

Abstract: The paper addresses the problem of solving classic distributed algorithmic problems under the practical model of Broadcast Communication Networks. Our main result is a new Leader Election algorithm, with O(n) time complexity and O(n · lg(n)) message transmission complexity. Our distributed solution uses a special form of the propagation of information with feedback (PIF) building block tuned to the broadcast media, and a special counting and joining approach for the election procedure phase. The latter is required for achieving the linear time.

Distributed Learning, Communication Complexity and Privacy

Abstract: We consider the problem of PAC-learning from distributed data and analyze fundamental communication complexity questions involved. We provide general upper and lower bounds on the amount of communication needed to learn well, showing that in addition to VC-dimension and covering number, quantities such as the teaching-dimension and mistake-bound of a class play an important role. We also present tight results for a number of common concept classes including conjunctions, parity functions, and decision lists. For linear separators, we show that for non-concentrated distributions, we can use a version of the Perceptron algorithm to learn with much less communication than the number of updates given by the usual margin bound. We also show how boosting can be performed in a generic manner in the distributed setting to achieve communication with only logarithmic dependence on 1/epsilon for any concept class, and demonstrate how recent work on agnostic learning from class-conditional queries can be used to achieve low communication in agnostic settings as well. We additionally present an analysis of privacy, considering both differential privacy and a notion of distributional privacy that is especially appealing in this context.