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This approach finds multiple network routes by using a minimum path cost.
For nodes u, v ∈ V, denote by d u, v f the minimum cost of a path from u to v in G f, and for u, v ∈ V ^, denote by d ^ u, v f the minimum cost of a path from u to v in Ĝ f (if there is no path between u and v in one of these graphs, define the corresponding minimum path cost to be ∞).
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Nevertheless, this may be overcome by setting the initial labels of all nodes v ∈ V to the corresponding minimum path costs d s, v in the graph G of N. Since G is acyclic, these initial costs can be computed in O(| V| + | E|) = O(n) time using a simple topological traversal (see e.g., [ 43]).
It is thus possible to stop the flow algorithm upon the first iteration at which the minimum augmentation path cost is zero, where the flow at this stage is a minimum-cost flow which is not necessarily of maximum size (while it has the same cost as a min-cost max-flow).
Keeping the same parameters, minimum hop count path cost is also same as of GA cost, and thus, the path selected through minimum hop count metric is also an optimal path.
Keeping the same parameters, minimum hop count path cost is more than that of GA cost, and thus, the path selected through minimum hop count metric is not an optimal path.
Keeping the same parameters, minimum hop count path cost is more than that of GA cost, and thus, the path selected through minimum hop count metric is not optimal.
Fig. 8 Comparative results of minimum hop count path cost versus optimal path cost on 50 nodes WMN.
Fig. 4 Optimal path cost versus minimum hop count path cost for GA model 1.
Fig. 7 Optimal path cost versus minimum hop count path cost for GA model 4 Table 12 Experimental parameters Nodes Population Generations 50 500 1000.
Fig. 5 Optimal path cost versus minimum hop count path cost for GA model 2. GA model 3 (depicted in Table 8) is applied on "50 nodes WMN".
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