## The price of being near-sighted (2006)

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Venue: | In SODA ’06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm |

Citations: | 57 - 11 self |

### BibTeX

@INPROCEEDINGS{Kuhn06theprice,

author = {Fabian Kuhn and Thomas Moscibroda and Roger Wattenhofer},

title = {The price of being near-sighted},

booktitle = {In SODA ’06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm},

year = {2006},

pages = {980--989},

publisher = {ACM}

}

### Years of Citing Articles

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### Abstract

Achieving a global goal based on local information is challenging, especially in complex and large-scale networks such as the Internet or even the human brain. In this paper, we provide an almost tight classification of the possible trade-off between the amount of local information and the quality of the global solution for general covering and packing problems. Specifically, we give a distributed algorithm using only small messages which obtains an (ρ∆) 1/k-approximation for general covering and packing problems in time O(k 2), where ρ depends on the LP’s coefficients. If message size is unbounded, we present a second algorithm that achieves an O(n 1/k) approximation in O(k) rounds. Finally, we prove that these algorithms are close to optimal by giving a lower bound on the approximability of packing problems given that each node has to base its decision on information from its k-neighborhood. 1

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Citation Context ...ithms targeted for specific covering and packing problems include algorithms for the minimum dominating set problem [3, 9, 22] as well as algorithms for maximal matchings and maximal independent sets =-=[1, 8, 16]-=-. This implies a constant approximation for maximum matching. All described distributed algorithms have a time complexity which is at least logarithmic in n. That is, each node may gather information ... |

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Citation Context ...ithms targeted for specific covering and packing problems include algorithms for the minimum dominating set problem [3, 9, 22] as well as algorithms for maximal matchings and maximal independent sets =-=[1, 8, 16]-=-. This implies a constant approximation for maximum matching. All described distributed algorithms have a time complexity which is at least logarithmic in n. That is, each node may gather information ... |

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Citation Context ... models. In various papers, researchers have investigated the “price of anarchy,” which is the degradation of a globally optimal solution if the individuals of the network perform in a selfish manner =-=[23, 24]-=-. In this paper, we analyze the degradation of a globally optimal solution if each individual’s knowledge is restricted to its neighborhood or local environment. We hope that this paper makes a step t... |

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Citation Context ...problems that can be formulated as packing and covering LPs. There are a number of algorithms for solving such LPs which are faster than interiorpoint methods that can be applied to general LPs (e.g. =-=[6, 7, 17, 21]-=-). All these algorithms need global information to work. The problem of approximating positive LPs using only local information has been introduced in [19]. The first algorithm achieving a constant ap... |

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Citation Context ...ithms targeted for specific covering and packing problems include algorithms for the minimum dominating set problem [3, 9, 22] as well as algorithms for maximal matchings and maximal independent sets =-=[1, 8, 16]-=-. This implies a constant approximation for maximum matching. All described distributed algorithms have a time complexity which is at least logarithmic in n. That is, each node may gather information ... |

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