Appendix
7.1
Matlab code
7.1.1
Dijstra’s algorithm
function [spcost, path] = dijkstra9(costmatrix, s, d)
%=================================================================== % inputs:
% n*n costmatrix
% n: the number of nodes in the network; % s: source node index;
% d: destination node index;
%=================================================================== n=size(costmatrix,1);
% vector, set of visited vectors S(1:n) = 0;
% it stores the shortest distance between the source node and any other node; dist(1:n) = inf;
% Previous node,
%informs about the best previous node known to reach each network node prev(1:n) = n+1; dist(s) = 0; while sum(S)~=n candidate=[]; for i=1:n if S(i)==0 candidate=[candidate dist(i)];
else candidate=[candidate inf]; end end [u_index u]=min(candidate); S(u)=1; for i=1:n if costmatrix(u,i)>0 if(dist(u)+costmatrix(u,i))<dist(i) dist(i)=dist(u)+costmatrix(u,i); prev(i)=u; end end end end spcost = dist(d); path = prev
7.1.2
Floyd-Warshall algorithm
function [new, path] = floyd(costmatrix)
%==================================================== % inputs:
% n*n costmatrix
%n the amount of nodes in the network
%==================================================== n=size(costmatrix,1);
%Define the elements of the weight matrix as w %and the elements of the path matrix as pred for u = 1:n for v = 1:n w(u,v) = costmatrix(u,v); pred(u,v) = v; end end
%Test to see if inequality hold for v1 =1:n
for v = 1:n if w(u,v1) + w(v1,v) < w(u,v) w(u,v) = w(u,v1) + w(v1,v); pred(u,v) = v1; end end end end
%Construct the new weight and path matrices new = w;
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