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# Week13 lec1

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### Week13 lec1

1. 1. Chapter 4 Network Layer Computer Networking: A Top Down Approach 4th edition. Jim Kurose, Keith Ross Addison-Wesley, July 2007.
2. 2. Routing Protocols • Define how routers exchange network information – What type of information – The format of information exchange – When to exchange – Which router to exchange information with • Examples – Routing Information Protocol (RIP) – Enhanced Interior Gateway Routing Protocol (EIGRP) – CISCO Proprietary – Open Shortest Path First (OSPF) – Border Gateway Protocol (BGP)
3. 3. Routing Algorithms Given a set of routers a routing algorithm finds a “Good” path from source router to destination router Least cost path routing algorithm local forwarding table header value output link 0100 0101 0111 1001 A graph is used to formulate routing problems A Graph G=(N,E) is a Set of N nodes and a collection E of edges Nodes in the graph represent Routers Edges represent physical links 3 2 2 1 packet’s header 0111 1 3 2
4. 4. Graph Abstraction 5 2 u v 2 1 x 3 w 3 1 5 z 1 y 2 Graph: G = (N,E) N = set of routers = { u, v, w, x, y, z } E = set of links ={ (u,v), (u,x), (v,x), (v,w), (x,w), (x,y), (w,y), (w,z), (y,z) }
5. 5. Graph Abstraction: costs 5 2 u v 2 1 x • c(x,x‟) = cost of link (x,x‟) 3 w 3 1 5 z 1 y 2 - e.g., c(w,z) = 5 • Cost can be •Physical length of the link •Delay etc. Cost of path (x1, x2, x3,…, xp) = c(x1,x2) + c(x2,x3) + … + c(xp-1,xp) Question: What‟s the least-cost path between u and z ? Routing algorithm: Algorithm that finds least-cost path
6. 6. Routing Algorithm Classification Global Routing Algorithm Decentralized Routing Algorithm  Computes least cost path  No node has complete     using complete global knowledge about the network. Takes connectivity between all nodes and all link costs as input. All routers have complete topology, link cost information Also called “Link State” Algorithms Used by Open Shortest Path First Protocol (OSPF)     information about the cost of all links. In the beginning knowledge of its own directly attached links. Computes least cost path by an iterative process of calculation and exchange of information. Also called Distance Vector (DV) Algorithm Used by Routing Information Protocol (RIP)
7. 7. Link-State Routing Algorithm  Network topology and link costs are known to all nodes  Each node broadcast link state packets to all other nodes in the network  Each link state packet contains the identities and cost of its attached links Dijkstra‟s Algorithm  Computes least cost paths from one node („source”) to all other nodes  Iterative: After k iterations, least cost paths to k destinations are known Notation:  D(v): Current value of least cost path from source to destination (v).  p(v): Predecessor node along path from source to v  N': Subset of nodes whose least cost path is definitively known
8. 8. Dijkstra‟s Algorithm: Example Step 0 1 2 3 4 5 N' u ux uxy uxyv uxyvw uxyvwz D(v),p(v) D(w),p(w) 2,u 5,u 2,u 4,x 2,u 3,y 3,y 5 2 u v 2 1 x D(x),p(x) 1,u D(y),p(y) ∞ 2,x D(z),p(z) ∞ ∞ 4,y 4,y 4,y Resulting forwarding table in u: 3 w 3 1 5 z 1 y destination 2 link x (u,x) y (u,x) v w z (u,v) (u,x) (u,x)
9. 9. Dijkstra‟s Algorithm 5 1 Initialization: 3 v w 2 N' = {u} 2 3 for all nodes v u 2 1 4 if v is a neighbor of u 3 1 5 then D(v) = c(u,v) x y 1 6 else D(v) = ∞ 7 8 Loop 9 find w not in N' such that D(w) is a minimum 10 add w to N' 11 update D(v) for each neighbor v of w and not in N' : 12 D(v) = min( D(v), D(w) + c(w,v) ) 13 /* new cost to v is either old cost to v or known 14 shortest path cost to w plus cost from w to v */ 15 until all nodes in N' 5 z 2
10. 10. Dijkstra‟s Algorithm-Example Find the shortest path from S to all nodes using Dijkstra‟s Algorithm?
11. 11. Solution Step 0 N’ s D(x), p(x) D(t),p(t) D(u),p(u) D(v),p(v) D(w),p(w) D(y),p(y) D(z),p(z) ∞ 1,s 4,s ∞ ∞ ∞ ∞ 1 st ∞ 3,t 5,t ∞ 8,t 6,t 2 stu ∞ 5,t 6,u 8,t 6,t 3 stuv 8,v 6,u 6,v 6,t 4 stuvy 8,v 6,u 5 stuvyz 8,v 6,u 6 stuvyzw 8,v 7 stuvyzwx 6,t
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