Fast Distributed Algorithms for Computing Separable Functions

The problem of computing functions of values at the nodes in a network in a fully distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer, and ad hoc networks. The task of computing separable functions...

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Vydáno v:IEEE transactions on information theory Ročník 54; číslo 7; s. 2997 - 3007
Hlavní autoři: Mosk-Aoyama, D., Shah, D.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY IEEE 01.07.2008
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Ad hoc networks
Algorithm design and analysis
Algorithms
Applied sciences
Computation
Computer networks
Data aggregation
Distributed algorithms
Distributed computing
Electronics
Exact sciences and technology
Functions
gossip algorithms
Graphs
Grid computing
Information theory
Information, signal and communications theory
Iterative algorithms
Mathematical analysis
Mathematical models
Network topology
Peer to peer computing
Protocols
Randomized algorithms
Running
Spectra
Studies
Subroutines
Telecommunications
Telecommunications and information theory
Teleprocessing networks. Isdn
Valuation and optimization of characteristics. Simulation
Averaging method
Peer to peer
Subroutine
Wireless telecommunication
Data aggregation
Iterative method
gossip algorithms
Resource sharing
Distributed computing
Linear combination
Computer network
distributed algorithms
randomized algorithms
Distributed algorithm
Fast algorithm
Ad hoc network
ISSN:0018-9448, 1557-9654
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Popis
Shrnutí:The problem of computing functions of values at the nodes in a network in a fully distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer, and ad hoc networks. The task of computing separable functions, which can be written as linear combinations of functions of individual variables, is studied in this context. Known iterative algorithms for averaging can be used to compute the normalized values of such functions, but these algorithms do not extend, in general, to the computation of the actual values of separable functions. The main contribution of this paper is the design of a distributed randomized algorithm for computing separable functions. The running time of the algorithm is shown to depend on the running time of a minimum computation algorithm used as a subroutine. Using a randomized gossip mechanism for minimum computation as the subroutine yields a complete fully distributed algorithm for computing separable functions. For a class of graphs with small spectral gap, such as grid graphs, the time used by the algorithm to compute averages is of a smaller order than the time required by a known iterative averaging scheme.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2008.924648