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MIT16_36s09_lec23_24

MIT16_36s09_lec23_24 - MIT OpenCourseWare http/ocw.mit.edu...

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MIT OpenCourseWare http://ocw.mit.edu 16.36 Communication Systems Engineering Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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Routing in Data Networks Eytan Modiano Eytan Modiano Slide 1
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Packet Switched Networks Packet Network PS PS PS PS PS PS PS Buffer Packet Switch Messages broken into Packets that are routed To their destination Eytan Modiano Slide 2
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Routing Must choose routes for various origin destination pairs (O/D pairs) or for various sessions Datagram routing: route chosen on a packet by packet basis Using datagram routing is an easy way to split paths Virtual circuit routing: route chosen a session by session basis Static routing: route chosen in a prearranged way based on O/D pairs Eytan Modiano Slide 3
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Broadcast Routing Route a packet from a source to all nodes in the network Possible solutions: Flooding: Each node sends packet on all outgoing links Discard packets received a second time Spanning Tree Routing: Send packet along a tree that includes all of the nodes in the network Eytan Modiano Slide 4
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Graphs A graph G = (N,A) is a finite nonempty set of nodes and a set of node pairs A called arcs (or links or edges) 1 2 3 4 1 2 3 N = {1,2,3} A = {(1,2)} N = {1,2,3,4} A = {(1,2),(2,3),(1,4),(2,4)} Eytan Modiano Slide 5
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Walks and paths A walk is a sequence of nodes (n 1 , n 2 , ...,n k ) in which each adjacent node pair is an arc A path is a walk with no repeated nodes 1 2 4 3 1 2 4 3 Walk (1,2,3,4,2) Path (1,2,3,4) Eytan Modiano Slide 6
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Cycles A cycle is a walk (n 1 , n 2 ,...,n k ) with n 1 = n k , k > 3, and with no repeated nodes except n 1 = n k 1 2 4 3 Cycle (1,2,4,3,1) Eytan Modiano Slide 7
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Connected graph A graph is connected if a path exists between each pair of nodes Connected Unconnected 1 2 4 3 1 2 3 An unconnected graph can be separated into two or more connected components Eytan Modiano Slide 8
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Acyclic graphs and trees An acyclic graph is a graph with no cycles A tree is an acyclic connected graph 1 2 4 3 1 2 3 1 2 3 Acyclic, unconnected Cyclic, connected not tree not tree The number of arcs in a tree is always one less than the number of nodes Proof: start with arbitrary node and each time you add an arc you add a node N nodes and N-1 links. If you add an arc without adding a node, the arc must go to a node already in the tree and hence form a cycle Eytan Modiano Slide 9
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Sub-graphs G' = (N',A') is a sub-graph of G = (N,A) if 1) G' is a graph 2) N' is a subset of N 3) A' is a subset of A One obtains a sub-graph by deleting nodes and arcs from a graph Note: arcs adjacent to a deleted node must also be deleted 1 2 4 3 1 2 3 Graph G Subgraph G' of G Eytan Modiano Slide 10
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Spanning trees T = (N',A') is a spanning tree of G = (N,A) if T is a sub-graph of G with N' = N and T is a tree 1 2 4 3 5 1 2 4 3 5 Graph G Spanning tree of G Eytan Modiano Slide 11
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