Perform the Dijkstra's algorithm on a network topology from a source node (shortest path to all remaining nodes).
[d,p] = NARVAL_M_Dijkstra(nx,ny,h,t,nd)
nodes x-coordinates.
nodes y-coordinates.
links head vector.
links tail vector.
source node.
distance vector from the source node towards remaining network nodes.
predecessor vector to reach the source node from remaining network nodes.
NARVAL_M_Dijkstra performs the Dijkstra's Algorithm from the source node nd on the network topology represented by the 4 following vectors: nx, ny, h and t. d and p enable to reconstruct the shortest path between any network node towards the source node ni (WIKIPEDIA).
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=80;//network size L=1000;//network square area side dmax=100;//locality radius [g]=NARVAL_T_LocalityConnex(n,L,dmax);//generation of a random topology in respect with the Locality method. i=NARVAL_F_Random(length(g.node_x));//selection of the source node ind=1;//window index [f]=NARVAL_G_ShowNodesIndex(g,ind); [dist,pred]=NARVAL_M_Dijkstra(g.node_x,g.node_y,g.head,g.tail,i);//application of NARVAL_M_Dijkstra i dist pred | ![]() | ![]() |
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