## Computing 2-Hop Neighborhoods in Ad Hoc Wireless Networks (2003)

Venue: | In ADHOC-NOW’03 |

Citations: | 37 - 0 self |

### BibTeX

@INPROCEEDINGS{Calinescu03computing2-hop,

author = {Gruia Calinescu},

title = {Computing 2-Hop Neighborhoods in Ad Hoc Wireless Networks},

booktitle = {In ADHOC-NOW’03},

year = {2003},

pages = {175--186}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present efficient distributed algorithms for computing 2-hop neighborhoods in Ad Hoc Wireless Networks. The knowledge of the 2-hop neighborhood is assumed in many protocols and algorithms for routing, clustering, and distributed channel assignment, but no efficient distributed algorithms for computing the 2-hop neighborhoods were previously published. The problem is nontrivial,...

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Citation Context ...wise distance. Probing - lowering the transmission power over an interval of time - is one way which allows the computation of pairwise distances. A detailed discussion of location systems appears in =-=[13]-=-. Under this assumption, we present a distributed algorithm which allows every node to compute its 2-hop neighborhood. The total number of messages of the algorithm is O(n). The algorithm is based on ... |

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Citation Context ...ith one endpoint in N 1 (v) and the other endpoint in N 2 (v) are included. Knowledge of the 2-hop neighborhoods is assumed in many distributed algorithm and protocols such as constructing structures =-=[24, 6]-=-, improved routing [20], broadcasting [9], and channel assignment [3]. The clusters used for channel control typically have diameter at most two [19]. The knowledge of the set of 2-hop neighbors is he... |

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Citation Context ...roduced by Alzoubi, Wan, and Frieder [2, 21]. This connected dominating set is based on a maximal independent set (MIS), whose role in algorithms for unit-disk graphs was discovered by Marathe et. al =-=[16]-=-. An MIS is a dominating set: every node must have a 1-hop neighbor in the maximal independent set. In our algorithm, each node uses its adjacent node(s) in the MIS to broadcast over a larger area rel... |

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Citation Context ...m and protocols such as constructing structures [24, 6], improved routing [20], broadcasting [9], and channel assignment [3]. The clusters used for channel control typically have diameter at most two =-=[19]-=-. The knowledge of the set of 2-hop neighbors is helpful in frequency assignment to avoid secondary interference. Also distributed algorithms for L(2; 1)-Labeling ([12, 8, 10]) can use the information... |

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Citation Context ...he algorithm is O(n). The algorithm is based on triangulation 2-Hop Neighborhoods 3 and can be immediatly updated to work when the angle-of-arrival information is available (an assumption justied in [=-=18-=-] or [15]) instead of pairwise distances. Our approach is based on the specic connected dominating set introduced by Alzoubi, Wan, and Frieder [2, 21]. This connected dominating set is based on a maxi... |

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Citation Context ...cally have diameter at most two [19]. The knowledge of the set of 2-hop neighbors is helpful in frequency assignment to avoid secondary interference. Also distributed algorithms for L(2; 1)-Labeling (=-=[12, 8, 10]-=-) can use the information about 2-hop neighborhoods stored by every node. Knowledge of the 2-hop neighborhood can be used for ecient computation of multipoint relays, used for example in [14]. Our dis... |

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Citation Context ...ms which have higher communication complexity on unit-disk graphs than on embedded (nodes aware of their geographical position) unit-disk graphs. Note that it is NP-Hard to recognize unit-disk graphs =-=[7]-=-. However, it follows from standard algebraic geometry results (page 542 of [17] or improved bounds in [4]) that the number of labeled unit-disk graphs of n nodes is between 2 c1 n log n and 2 c2 n lo... |

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Citation Context ...he virtual backbone with at most three times as many links from an MIS node adjacent to the origin of the path to an MIS node adjacent to the destination of the path. This fact was noticed by Alzoubi =-=[1]-=-, and by Wang and Li [22], which also planarize the virtual backbone while keeping all its attractive properties. 3 Geographic Position Available In this section we describe the distributed algorithm ... |

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Citation Context ...point in N 2 (v) are included. Knowledge of the 2-hop neighborhoods is assumed in many distributed algorithm and protocols such as constructing structures [24, 6], improved routing [20], broadcasting =-=[9]-=-, and channel assignment [3]. The clusters used for channel control typically have diameter at most two [19]. The knowledge of the set of 2-hop neighbors is helpful in frequency assignment to avoid se... |

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Citation Context ...cally have diameter at most two [19]. The knowledge of the set of 2-hop neighbors is helpful in frequency assignment to avoid secondary interference. Also distributed algorithms for L(2; 1)-Labeling (=-=[12, 8, 10]-=-) can use the information about 2-hop neighborhoods stored by every node. Knowledge of the 2-hop neighborhood can be used for ecient computation of multipoint relays, used for example in [14]. Our dis... |

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Citation Context ...ded (nodes aware of their geographical position) unit-disk graphs. Note that it is NP-Hard to recognize unit-disk graphs [7]. However, it follows from standard algebraic geometry results (page 542 of =-=[17]-=- or improved bounds in [4]) that the number of labeled unit-disk graphs of n nodes is between 2 c1 n log n and 2 c2 n log n , for constants c 1 and c 2 and therefore a protocol with a total O(n log n)... |

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Citation Context ...ithm is O(n). The algorithm is based on triangulation 2-Hop Neighborhoods 3 and can be immediatly updated to work when the angle-of-arrival information is available (an assumption justied in [18] or [=-=15-=-]) instead of pairwise distances. Our approach is based on the specic connected dominating set introduced by Alzoubi, Wan, and Frieder [2, 21]. This connected dominating set is based on a maximal inde... |

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Citation Context ... information is available (an assumption justied in [18] or [15]) instead of pairwise distances. Our approach is based on the specic connected dominating set introduced by Alzoubi, Wan, and Frieder [2=-=, 21]-=-. This connected dominating set is based on a maximal independent set (MIS), whose role in algorithms for unit-disk graphs was discovered by Marathe et. al [16]. An MIS is a dominating set: every node... |

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Citation Context ... ([12, 8, 10]) can use the information about 2-hop neighborhoods stored by every node. Knowledge of the 2-hop neighborhood can be used for ecient computation of multipoint relays, used for example in =-=[14]-=-. Our distributed algorithms operate in an asynchronous environment, and we use the number of messages as the measure of the eciency of the algorithm. In our model a message can hold the ID of a node,... |

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Citation Context ...cally have diameter at most two [19]. The knowledge of the set of 2-hop neighbors is helpful in frequency assignment to avoid secondary interference. Also distributed algorithms for L(2; 1)-Labeling (=-=[12, 8, 10]-=-) can use the information about 2-hop neighborhoods stored by every node. Knowledge of the 2-hop neighborhood can be used for ecient computation of multipoint relays, used for example in [14]. Our dis... |

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Citation Context ...ith one endpoint in N 1 (v) and the other endpoint in N 2 (v) are included. Knowledge of the 2-hop neighborhoods is assumed in many distributed algorithm and protocols such as constructing structures =-=[24, 6]-=-, improved routing [20], broadcasting [9], and channel assignment [3]. The clusters used for channel control typically have diameter at most two [19]. The knowledge of the set of 2-hop neighbors is he... |

5 |
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Citation Context ...eographical position) unit-disk graphs. Note that it is NP-Hard to recognize unit-disk graphs [7]. However, it follows from standard algebraic geometry results (page 542 of [17] or improved bounds in =-=[4]-=-) that the number of labeled unit-disk graphs of n nodes is between 2 c1 n log n and 2 c2 n log n , for constants c 1 and c 2 and therefore a protocol with a total O(n log n) bits communication comple... |

2 |
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Citation Context ... information is available (an assumption justied in [18] or [15]) instead of pairwise distances. Our approach is based on the specic connected dominating set introduced by Alzoubi, Wan, and Frieder [2=-=, 21]-=-. This connected dominating set is based on a maximal independent set (MIS), whose role in algorithms for unit-disk graphs was discovered by Marathe et. al [16]. An MIS is a dominating set: every node... |

2 |
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Citation Context ...) and the other endpoint in N 2 (v) are included. Knowledge of the 2-hop neighborhoods is assumed in many distributed algorithm and protocols such as constructing structures [24, 6], improved routing =-=[20]-=-, broadcasting [9], and channel assignment [3]. The clusters used for channel control typically have diameter at most two [19]. The knowledge of the set of 2-hop neighbors is helpful in frequency assi... |

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1 |
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Citation Context ...ghbors such that a system of coordinates can be locally established and in which the position of every node of the rigid piece is completely dened. A theory of geometric rigidity is well established [=-=23]-=-. We need only simple properties which are easily proved below. 2-Hop Neighborhoods 7 First we describe the distributed algorithm for computing the rigid pieces. Before the actual construction, every ... |