By Maia Fraser (auth.), Evangelos Kranakis, Jaroslav Opatrny (eds.)
This ebook constitutes the refereed lawsuits of the sixth overseas convention on Ad-Hoc Networks and instant, ADHOC-NOW 2007, held in Morelia, Mexico, in September 2007.
The 21 revised complete papers have been rigorously reviewed and chosen from 50 submissions. The papers are geared up in topical sections on routing, topology keep watch over, defense and privateness, protocols, in addition to caliber of provider and performance.
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Additional info for Ad-Hoc, Mobile, and Wireless Networks: 6th International Conference, ADHOC-NOW 2007, Morelia, Mexico, September 24-26, 2007, Proceeedings
Theorem 3. Let s and t be nodes in G and let be the length of a shortest Euclidean st-path in G. If GOAFR+ is used as the geographic routing algorithm A in Route2, then the Euclidean distance traveled by a message routed from s to t using Route2 is O( 2 ). d Proof. If s and t are such that s − t 2 ≤ 3√ then Lemma 5 tells us that s and 2 t are in a cell C. In this case, Algorithm Route2 uses W L(G[C]) to route the message from s to t. By construction, W L(G[C]) is guaranteed to be planar and contain a path of Euclidean length at most c · for some constant c.
Therefore, if GOAFR+ is used to route the message from s to t in W L(G[C]), the message travels O((c )2 ) = O( 2 ) Euclidean distance. d If s − t 2 > 3√ , then Lemma 6 tells us that there exists a path L = (s = 2 z0 , z1 , z2 , . . , zp = t) whose Euclidean length is at most β · for some constant β. Now consider the subpaths L1 , L2 , and L3 of L, and let 1 , 2 , and 3 respectively be the Euclidean lengths of these subpaths. Let C be the blue cell containing s. Since L1 is a path from s = z0 to zi in W L(G[C]) and since Algorithm Route2 routes from s = z0 to zi using GOAFR+ on the graph W L(G[C]), the message travels a distance of O( 21 ) from s to zi .
Topology Control and Geographic Routing in Realistic Wireless Networks 27 Algorithm BuildRoutingGraph √ Input: G = d-QUDG with d ≥ 1/ 2 Output: Routing Graph GR 1. Place a blue grid of √d2 × √d2 cells passing through (0, 0), a red grid of √d2 × √d2 d d cells passing through ( 3√ , √ ), and a green grid of √d2 × √d2 cells passing 2 3 2 √ , 2d √ ). through ( 32d 2 3 2 2. For each edge e in G initialize color(e) to the empty set. 3. For each non-empty grid cell C in each grid, construct the Wang-Li spanner W L(G[C]).
Ad-Hoc, Mobile, and Wireless Networks: 6th International Conference, ADHOC-NOW 2007, Morelia, Mexico, September 24-26, 2007, Proceeedings by Maia Fraser (auth.), Evangelos Kranakis, Jaroslav Opatrny (eds.)