Perform the shortest path between two network nodes on a topology in respect with the Dijkstra's algorithm.
[p] = NARVAL_R_Dijkstra_i_j(g,i,j)
network graph.
emission node.
destination node.
route between i and j.
NARVAL_R_Dijkstra_i_j performs the shortest path between the two nodes i and j of the graph g (WIKIPEDIA). p corresponds to the shortest path composed by a succession of nodes between i and j.
1 function Dijkstra(Graph, source): 2 for each vertex v in Graph: // Initializations 3 dist[v] := infinity // Unknown distance function from source to v 4 previous[v] := undefined // Previous node in optimal path from source 5 dist[source] := 0 // Distance from source to source 6 Q := the set of all nodes in Graph // All nodes in the graph are unoptimized - thus are in Q 7 while Q is not empty: // The main loop 8 u := vertex in Q with smallest dist[] 9 if dist[u] = infinity: 10 break // all remaining vertices are inaccessible from source 11 remove u from Q 12 for each neighbor v of u: // where v has not yet been removed from Q. 13 alt := dist[u] + dist_between(u, v) 14 if alt is inferior to dist[v]: // Relax (u,v,a) 15 dist[v] := alt 16 previous[v] := u 17 return dist[] | ![]() | ![]() |
n=150;//network size L=1000;//network square area side dmax=100;//Locality radius [g]=NARVAL_T_LocalityConnex(n,L,dmax);//generation of a topology in respect with the Locality method nf=length(g.node_x);//real network size nl=length(g.head);//quantity of network links [i,j]=NARVAL_F_Random_i_j(nf);//selection of the extremal nodes [path]=NARVAL_R_Dijkstra_i_j(g,i,j);//application of NARVAL_R_Dijkstra_i_j [p]=NARVAL_G_Nodes2Path(path,g);//set of links belonging to the shortest path Ebi=2;//width EC=ones(1,nl);//display the path between i and j EB=Ebi*ones(1,nl);//edge width EC(p)=5;//color EB(p)=2*Ebi; Bdi=5;//border D=Bdi*ones(1,nf);//node border D(path)=3*Bdi; g.node_border=D; g.edge_color=EC; g.edge_width=EB; ind=1;//window index [f]=NARVAL_G_ShowNodesIndex(g,ind);//graph visualization path | ![]() | ![]() |
Dr. Foued Melakessou
Research Associate
Interdisciplinary Centre for Security, Reliability and Trust
Room F106
University of Luxembourg
6, rue Coudenhove Kalergi
L-1359 Luxembourg-Kirchberg
E-mail: foued.melakessou@uni.lu
Tel: (+352) 46 66 44 5346