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set link cost as function of average utilization Least Cost Algorithms
Least basis for routing decisions defines cost of path between two nodes as sum
fines
of costs of links traversed
of in network of nodes connected by bidirectional links
where each link has a cost in each direction for each pair of nodes, find path with least cost can minimize hop with each link cost 1
or have link value inversely proportional to capacity nb. link costs in different directions may be different alternatives: Dijkstra or BellmanFord algorithms
alternatives: Dijkstra Dijkstra’s Algorithm
Dijkstra’s finds shortest paths from given source
finds node s to all other nodes by developing paths in order of increasing
by
path length
path algorithm runs in stages (next slide)
each time adding node with next shortest path
algorithm terminates when all nodes processed
by algorithm (in set T)
by Dijkstra’s Algorithm Method
Dijkstra’s Step 1 [Initialization]
Step Step 2 [Get Next Node]
Step [Get T = {s} Set of nodes so far incorporated
et
L(n) = w(s, n) for n ≠ s
initial path costs to neighboring nodes are simply link costs
find neighboring node not in T with leastcost path from s
find
with
incorporate node into T
also incorporate the edge that is incident on that node and a
also
node in T that contributes to the path
node Step 3 [Update LeastCost Paths]
Step [Update L(n) = min[L(n), L(x) + w(x, n)] for all n ∉ T
for
f llatter term is minimum, path from s to n...
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 Spring '09
 Mr.Ehab
 Graph Theory, Shortest path problem

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