#### DMCA

## Network computing capacity for the reverse butterfly network

### Citations

1920 | Network information flow
- Ahlswede, Cai, et al.
(Show Context)
Citation Context ...f computation, that is the maximum number of times the specified function can be computed per network usage. In [2], we presented a network computation model that is closely related to network coding =-=[1]-=-, [13], thus extending network “coding” to network “computing”. Network coding with a single receiver is equivalent to the special case of network computing when the function to be computed is the (ve... |

748 | Communication complexity
- Kushilevitz, Nisan
- 1997
(Show Context)
Citation Context ...ed only the existence of a solution, rather than the rate at which the solution can be computed. Problems related to function computation have been studied in a such areas as communication complexity =-=[8]-=-, [12], average consensus [4], [6], and distributed computation [3], [10]. The reader is referred to [7] for a review of various approaches to the problem. The model we use is concerned with the maxim... |

513 | Randomized gossip algorithms
- Boyd, Ghosh, et al.
- 2006
(Show Context)
Citation Context ...lution, rather than the rate at which the solution can be computed. Problems related to function computation have been studied in a such areas as communication complexity [8], [12], average consensus =-=[4]-=-, [6], and distributed computation [3], [10]. The reader is referred to [7] for a review of various approaches to the problem. The model we use is concerned with the maximum possible rate of computing... |

488 |
Some complexity questions related to distributive computing (preliminary report
- Yao
- 1979
(Show Context)
Citation Context ...ly the existence of a solution, rather than the rate at which the solution can be computed. Problems related to function computation have been studied in a such areas as communication complexity [8], =-=[12]-=-, average consensus [4], [6], and distributed computation [3], [10]. The reader is referred to [7] for a review of various approaches to the problem. The model we use is concerned with the maximum pos... |

193 |
A First Course in Information Theory
- Yeung
- 2002
(Show Context)
Citation Context ...putation, that is the maximum number of times the specified function can be computed per network usage. In [2], we presented a network computation model that is closely related to network coding [1], =-=[13]-=-, thus extending network “coding” to network “computing”. Network coding with a single receiver is equivalent to the special case of network computing when the function to be computed is the (vector) ... |

109 | Geographic gossip: Efficient aggregation for sensor networks
- Dimakis, Sarwate, et al.
(Show Context)
Citation Context ...n, rather than the rate at which the solution can be computed. Problems related to function computation have been studied in a such areas as communication complexity [8], [12], average consensus [4], =-=[6]-=-, and distributed computation [3], [10]. The reader is referred to [7] for a review of various approaches to the problem. The model we use is concerned with the maximum possible rate of computing a gi... |

104 |
Complexity classification of network information flow problems
- Lehman, Lehman
(Show Context)
Citation Context ...e computed is the (vector) identity map - that is, the receiver wants to reproduce all of the messages generated by the sources. Routing is known to be rate-optimal for single receiver network coding =-=[9]-=-. We extend the network coding model to computation of arbitrary functions of source messages. Our work is related to that of Ramamoorthy [11], who studied computing the parity of a collection of bina... |

75 | Toward a theory of in-network computation in wireless sensor networks
- Gharavi, Kumar
- 2006
(Show Context)
Citation Context ...s related to function computation have been studied in a such areas as communication complexity [8], [12], average consensus [4], [6], and distributed computation [3], [10]. The reader is referred to =-=[7]-=- for a review of various approaches to the problem. The model we use is concerned with the maximum possible rate of computing a given function at a node where, the set of allowable interactions is con... |

55 | Fast Distributed Algorithms for Computing Separable Functions
- Mosk-Aoyama, Shah
(Show Context)
Citation Context ...olution can be computed. Problems related to function computation have been studied in a such areas as communication complexity [8], [12], average consensus [4], [6], and distributed computation [3], =-=[10]-=-. The reader is referred to [7] for a review of various approaches to the problem. The model we use is concerned with the maximum possible rate of computing a given function at a node where, the set o... |

38 | Network Routing Capacity
- Cannons, Dougherty, et al.
- 2006
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Citation Context ...habet A. In contrast, for ordinary network coding (i.e. when the target function is the identity map), the coding capacity and routing capacity are known to be independent of the coding alphabet used =-=[5]-=-. Remark II.5. The ratio of the coding capacity to the routing capacity for the multicast butterfly network with two messages is 4/3 (see [5]), i.e. coding provides an advantage of about 33%. The corr... |

24 | Communicating the sum of sources over a network
- Ramamoorthy
- 2008
(Show Context)
Citation Context ...nown to be rate-optimal for single receiver network coding [9]. We extend the network coding model to computation of arbitrary functions of source messages. Our work is related to that of Ramamoorthy =-=[11]-=-, who studied computing the parity of a collection of binary sources in a network with two sources and arbitrary number of receivers, or vice versa; however, he considered only the existence of a solu... |

15 | Network Coding for Computing
- Appuswamy, Franceschetti, et al.
- 2008
(Show Context)
Citation Context ...mputes a function of these messages. The objective is to characterize the maximum rate of computation, that is the maximum number of times the specified function can be computed per network usage. In =-=[2]-=-, we presented a network computation model that is closely related to network coding [1], [13], thus extending network “coding” to network “computing”. Network coding with a single receiver is equival... |

5 |
Lower bounds on information rates for distributed computation via noisy channels
- Ayaso, Shah, et al.
- 2007
(Show Context)
Citation Context ...the solution can be computed. Problems related to function computation have been studied in a such areas as communication complexity [8], [12], average consensus [4], [6], and distributed computation =-=[3]-=-, [10]. The reader is referred to [7] for a review of various approaches to the problem. The model we use is concerned with the maximum possible rate of computing a given function at a node where, the... |