Iyer, Srikanth K and Manjunath, D and Sundaresan, Rajesh
(2011)
*In-Network Computation in Random Wireless Networks: A PAC Approach to Constant Refresh Rates with Lower Energy Costs.*
In: IEEE Transactions on Mobile Computing, 10
(1).
pp. 146-155.

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## Abstract

We propose a method to compute a probably approximately correct (PAC) normalized histogram of observations with a refresh rate of Theta(1) time units per histogram sample on a random geometric graph with noise-free links. The delay in computation is Theta(root n) time units. We further extend our approach to a network with noisy links. While the refresh rate remains Theta(1) time units per sample, the delay increases to Theta(root n log n). The number of transmissions in both cases is Theta(n) per histogram sample. The achieved Theta(1) refresh rate for PAC histogram computation is a significant improvement over the refresh rate of Theta(1/log n) for histogram computation in noiseless networks. We achieve this by operating in the supercritical thermodynamic regime where large pathways for communication build up, but the network may have more than one component. The largest component however will have an arbitrarily large fraction of nodes in order to enable approximate computation of the histogram to the desired level of accuracy. Operation in the supercritical thermodynamic regime also reduces energy consumption. A key step in the proof of our achievability result is the construction of a connected component having bounded degree and any desired fraction of nodes. This construction may also prove useful in other communication settings on the random geometric graph.

Item Type: | Journal Article |
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Publication: | IEEE Transactions on Mobile Computing |

Publisher: | IEEE |

Additional Information: | Copyright 2011 IEEE. Personal use of this material is permitted.However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. |

Keywords: | Ad hoc network; wireless sensor network; function computation; PAC computation; percolation |

Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering Division of Physical & Mathematical Sciences > Mathematics |

Date Deposited: | 23 Dec 2010 09:36 |

Last Modified: | 23 Dec 2010 09:36 |

URI: | http://eprints.iisc.ac.in/id/eprint/34324 |

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