Topic
Communication complexity
About: Communication complexity is a research topic. Over the lifetime, 3870 publications have been published within this topic receiving 105832 citations.
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TL;DR: This work considers the problem of information aggregation in sensor networks, where one is interested in computing a function of the sensor measurements, and presents a cut-set lower bound and an achievable scheme based on aggregation along trees.
Abstract: We consider the problem of information aggregation in sensor networks, where one is interested in computing a function of the sensor measurements. We allow for block processing and study in-network function computation in directed graphs and undirected graphs. We study how the structure of the function affects the encoding strategies and the effect of interactive information exchange. Depending on the application, there could be a designated collector node, or every node might want to compute the function. We begin by considering a directed graph C = (γ. e) on the sensor nodes, where the goal is to determine the optimal encoders on each edge which achieve function computation at the collector node. Our goal is to characterize the rate region in R|e|, i.e., the set of points for which there exist feasible encoders with given rates which achieve zero-error computation for asymptotically large block length. We determine the solution for directed trees, specifying the optimal encoder and decoder for each edge. For general directed acyclic graphs, we provide an outer bound on the rate region by finding the disambiguation requirements for each cut, and describe examples where this outer bound is tight. Next, we address the scenario where nodes are connected in an undirected tree network, and every node wishes to compute a given symmetric Boolean function of the sensor data. Undirected edges permit interactive computation, and we therefore study the effect of interaction on the aggregation and communication strategies. We focus on sum-threshold functions and determine the minimum worst case total number of bits to be exchanged on each edge. The optimal strategy involves recursive in-network aggregation which is reminiscent of message passing. In the case of general graphs, we present a cut-set lower bound and an achievable scheme based on aggregation along trees. For complete graphs, we prove that the complexity of this scheme is no more than twice that of the optimal scheme.
67 citations
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01 Jan 1988TL;DR: This paper presents several end-toend communication protocols whose space complexity at each node is independent of either the input length or the network size, and dispel the myth ‘The sender and the receiver are not forever separated’.
Abstract: This paper addresses the problem of end-toend communication over a dynamically changing network in which the sender and the receiver are not forever separated. We present several end-to-end communication protocols whose space complexity at each node is independent of either the input length or the network size. Although the time complexity of these protocols is bounded, their communication complexity is either unbounded, or exponential if an acyclic orientation of the network is given. To bound the communication complexity of the protocols, in the absence of an acyclic orientation, we assume either knowledge of the total number of nodes in the network, or that nodes have unique ids. These bounded communication-complexity protocols thus require O(logn) space per incident link at each node. In sum, we dispel the myth ‘Supported by NSF Presidential Young Investigators Award under grant DCR84-51396 SL matching funds from IBM FacuRy Development Award under
67 citations
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TL;DR: It is proved that two-party randomized communication complexity satisfies a strong direct product property, so long as the communication lower bound is proved by a “corruption” or “one-sided discrepancy” method over a rectangular distribution.
Abstract: We prove that two-party randomized communication complexity satisfies a strong direct product property, so long as the communication lower bound is proved by a "corruption" or "one-sided discrepancy" method over a rectangular distribution. We use this to prove new n ?(1) lower bounds for 3-player number-on-the-forehead protocols in which the first player speaks once and then the other two players proceed arbitrarily. Using other techniques, we also establish an ?(n 1/(k?1)/(k ? 1)) lower bound for k-player randomized number-on-the-forehead protocols for the disjointness function in which all messages are broadcast simultaneously. A simple corollary of this is that general randomized number-on-the-forehead protocols require ?(log n/(k ? 1)) bits of communication to compute the disjointness function.
67 citations
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06 Jun 1994TL;DR: Algorithms for variable ordering for BDD representation of a system of interacting finite state machines are implemented in HSIS, a hierarchical synthesis and verification tool currently under development at Berkeley.
Abstract: We address the problem of obtaining good variable orderings for the BDD representation of a system of interacting finite state machines (FSMs). Orderings are derived from the communication structure of the system. Communication complexity arguments are used to prove upper bounds on the size of the BDD for the transition relation of the product machine in terms of the communication graph, and optimal orderings are exhibited for a variety of regular systems. Based on the bounds we formulate algorithms for variable ordering. We perform reached state analysis on a number of standard verification benchmarks to test the effectiveness of our ordering strategy; experimental results demonstrate the efficacy of our approach. The algorithms described in this paper have been implemented in HSIS, a hierarchical synthesis and verification tool currently under development at Berkeley.
67 citations
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TL;DR: Miltersen and Wigderson as discussed by the authors gave a new lower bound for the predecessor problem that matches the bounds of Beame and Fich, and used the round elimination approach to obtain a tight lower bound.
67 citations