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# Internet Protocols TCOM 509

Mason

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This 8 page Class Notes was uploaded by Dalton Gerhold on Monday September 28, 2015. The Class Notes belongs to TCOM 509 at George Mason University taught by Staff in Fall. Since its upload, it has received 37 views. For similar materials see /class/215145/tcom-509-george-mason-university in Telecommunications at George Mason University.

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Date Created: 09/28/15

TCOM 509 7 Fall 2003 Dr LiChuan Chen Dijkstra s Algorithm Example Given A network topology graph G with 6 nodes and the link cost between nodes as shown below m Using Dijkstra s Algorithm to nd the leastcost paths for nodes Athrough F Solution Let T A B C D E F number of nodes in the network s source node A N set of nodes that have been processed so far cij link cost from node i to node j if two nodes are directly connected 00 if there is no link between i and j DV cost of the shortest path least cost path from node s to node V that is currently known so far When the algorithm terminates DV is the cost of the shortest path from source s to destination V in the network PV predecessor node along path from source s to V that is next V l Initialization 0 N A initialize set N contains source node A 0 Compute DV for V is in set T but not in set N Need to Compute DV for V B C D E F v DM csv cAv PM TCOM 509 7 Fall 2003 Dr LiChuan Chen 2 Get Next Node 0 Find w not in N such that Dw is the minimum That is the smallest Dw in the previous step add that node w to set N If they are equal randomly pick one of them In this case DD l is the smallest so we add node w D to set N N A D TCOM 509 7 Fall 2003 Dr LiChuan Chen 3 Update Cost for the Shortest Paths DV min DV Dw cwv for all nodes V not in T min DV DD cDV for node V B C E F TCOM 509 7 Fall 2003 Dr LiChuan Chen 4 Get Next Node 0 Find w not in N such that Dw is the minimum That is the smallest Dw in the previous step add that node w to set N If they are equal randomly pick one of them In this case both DE and DB have the same smallest cost of 2 we randomly pick one We pick node w E to set N N A D E 5 Update Cost for the Shortest Paths DV min DV Dw cwv for all nodes V not in N min DV DE cEV for node V B C F TCOM 509 7 Fall 2003 Dr LiChuan Chen 6 Get Next Node 0 Find the smallest DV in the previous step add that node to N If they are equal randomly pick one of them DB has the lowest cost 2 We pick node w B to set N N A D E B 7 Update Cost for the Shortest Paths DV min DV Dw cwv for all nodes V not in N TCOM 509 7 Fall 2003 Dr LiChuan Chen min Dv DB cBV for node V C F v DM min I Dv D02 cBv I DM PM C DC minDC 2 cBC min3 23 3 E F DF minDF 2 cBF min4 2oo 4 E 8 Get Next Node 0 Find the smallest DV in the previous step add that node to N If they are equal pick any one of them DC is the smallest so we add node w C to set N NADEBC TCOM 509 7 Fall 2003 Dr LiChuan Chen 9 Update Cost for the Shortest Paths DV min DV Dw cwv for all node 11 not in N min DV DC cCV for node n F Iv DM min I DV DC cCvI Dv Pv F DF minDF 3 cCF mi 4 35 4 E 10 Get Next Node TCOM 509 7 Fall 2003 Dr LiChuan Chen 0 Find the smallest DV in the previous step add that node to N If they are equal pick any one of them DF is the only one so we add node w F to set N NADEBCF N T so the algorithm terminate 11 Now we have to write down the shortest path from node Ato all other nodes Start from backwards since those are the least cost for the shortest path and then work towards source node A The column DV is the cost for the shortest path from source Ato V

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