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Jorge Urrutia, IMATE-UNAM E. Chavez, S. Dobrev, E. Kranakis, V. Stacho, J. Opartny, S. Rajsbaum,

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## Jorge Urrutia, IMATE-UNAM E. Chavez, S. Dobrev, E. Kranakis, V. Stacho, J. Opartny, S. Rajsbaum,

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**Local Solutions for Global Problems in**Ad-hoc and Wireless Networks Jorge Urrutia, IMATE-UNAM E. Chavez, S. Dobrev, E. Kranakis, V. Stacho, J. Opartny, S. Rajsbaum, G. Salazar, H. Singh, I. Stojmenovic, J. Bose, P. Morin, …**Routing in Wireless Networks**v u The shortest path problem**Routing in Wireless Networks**Dijkstra’s algorithm v u The shortest path problem**Routing in Wireless Networks**Dijkstra’s algorithm v u Optimal solution but … For many current networks is not useful anymore The shortest path problem**Routing in Wireless Networks**Assumes: a) Stabel network. b) Full knowledge of the network topology Dijkstra’s algorithm v u Optimal solution but … For many current networks is not useful anymore The shortest path problem**b**Routing tables c d a**Other problems to consider:**b Routing tables Reliability, maintenance. c g d e f f g b c d e a**Other solutions:**b a b Message Hi! How are you? -------- -------- -------- -------- Flooding a**We would like routing algorithms of the following type:**a) Local algorithms Take decisions based only on local information stored at the nodes of the network b) No knowledge is assumed on the network other than it is connected**We would like routing algorithms of the following type:**a) Local algorithms Take decisions based only on local information stored at the nodes of the network b) No knowledge is assumed on the network other than it is connected c) Guarantees delivery of messages**We would like routing algorithms of the following type:**a) Local algorithms Take decisions based only on local information stored at the nodes of the network b) No knowledge is assumed on the network other than it is connected c) Guarantees delivery of messages d) Messages do not learn much, i.e. they have constant memory.**Interval Routing, Santoro and Khatib.**8 7 1 9 5 6 [1, 1] 2 [3, 9] 4 3**Interval Routing, Santoro and Khatib.**[9, 7] 8 8, 8] 7 1 [1, 8] 9 [9, 9] [1, 6] [2, 9] 5 [7, 9] [6,4] 6 [1, 5] [1, 1] 2 [6, 9] [5, 5] [3, 9] [1,2] [5, 3] 4 3 [4, 4]**An absent minded, almost memoryless tourist!**Shinjuku b a Arrives to Tokio without a map!**An absent minded, almost memoryless tourist!**Shinjuku b a Arrives to Tokio without a map!**An absent minded, almost memoryless tourist!**Shinjuku b a Arrives to Tokio without a map!**An absent minded, almost memoryless tourist!**Shinjuku b a Arrives to Tokio without a map!**An absent minded, almost memoryless tourist!**Shinjuku b a Arrives to Tokio without a map!**Compass routing**b a**Cellular networks** Delaunay triangulation**Cellular networks** Delaunay triangulation**Cellular networks** Delaunay triangulation**Cellular networks** Delaunay triangulation**Cellular networks** Delaunay triangulation**Cellular networks**Reliability Delaunay triangulation**Cellular networks**Reliability Delaunay triangulation**Cellular networks**Reliability Delaunay triangulation**Can we find a local algorithm at least for planar graphs?** **Face routing** **Face routing** **Face routing** **Face routing** **Face routing** **Face routing** **Face routing** **Face routing** **Face routing** **Face routing** **Face routing** **Face routing** **Face routing** **Face routing** **Face routing** **Face routing** **The Model: Unit distance graphs.**d=1 Points represent radio stations**Unit distance graphs are not planar!**The Gabriel subgraph v u Can we planarize them? Using a local algorithm?