Loops with random sampling from a matrix and distance calculation

I got a list of nodes, and I need to randomly assign 'p' hubs to 'n' clients.

I got the following data, where the first row shows:

• The total number of nodes.
• The requested number of hubs.
• The total supply capacity for each hub.

The following lines show:

• The first column the node number.
• The second column the "x" coordinate.
• The third the "y" coordinate.

The x and y values are provided so we can calculate the Euclidean distance.

nodes:

 50 5 120
 1 2 62 3
 2 80 25 14
 3 36 88 1
 4 57 23 14
 5 33 17 19
 6 76 43 2
 7 77 85 14
 8 94 6 6
 9 89 11 7
 10 59 72 6
 11 39 82 10
 12 87 24 18
 13 44 76 3
 14 2 83 6
 15 19 43 20
 16 5 27 4
 17 58 72 14
 18 14 50 11
 19 43 18 19
 20 87 7 15
 21 11 56 15
 22 31 16 4
 23 51 94 13
 24 55 13 13
 25 84 57 5
 26 12 2 16
 27 53 33 3
 28 53 10 7
 29 33 32 14
 30 69 67 17
 31 43 5 3
 32 10 75 3
 33 8 26 12
 34 3 1 14
 35 96 22 20
 36 6 48 13
 37 59 22 10
 38 66 69 9
 39 22 50 6
 40 75 21 18
 41 4 81 7
 42 41 97 20
 43 92 34 9
 44 12 64 1
 45 60 84 8
 46 35 100 5
 47 38 2 1
 48 9 9 7
 49 54 59 9
 50 1 58 2

I extracted the information from the first line.

nodes <- as.matrix(read.table(data))
header<-colnames(nodes)
clean_header <-gsub('X','',header)
requested_hubs <- as.numeric(clean_header[2])
max_supply_capacity <- as.numeric(clean_header[3])

I need to randomly select 5 nodes, that will act as hubs

set.seed(37)
node_to_hub <-nodes[sample(nrow(nodes),requested_hubs,replace = FALSE),]

Then randomly I need to assign nodes to each hub calculate the distances between the hub and each one of the nodes and when the max_supply_capacity(120) is exceeded select the following hub and repeat the process.

After the final iteration I need to return the cumulative sum of distances for all the hubs.

I need to repeat this process 100 times and return the min() value of the cumulative sum of distances.

This is where I'm completely stuck since I'm not sure how to loop through a matrix let alone when I have to select elements randomly.

I got the following elements:

capacity <- c(numeric()) # needs to be <= to 120
distance_sum <- c(numeric())
global_hub_distance <- c(numeric())

The formula for the euclidean distance (rounded) would be as below but I'm not sure how I can reflect the random selection when assigning nodes.

distance <-round(sqrt(((node_to_hub[i,2]-nodes[i,2]))^2+(node_to_hub[random,3]-nodes[random,3])^2))

The idea for the loop I think I need is below, but as I mentioned before I don't know how to deal with the sample client selection, and the distance calculation of the random clients.

    for(i in 1:100){
    node_to_hub
    for(i in 1:nrow(node_to_hub){
#Should I randomly sample the clients here???
    while(capacity < 120){ 
    node_demand <- nodes[**random**,3] 
    distance <-round(sqrt(((node_to_hub[i,2]-nodes[i,2]))^2+(node_to_hub[**random**,3]-nodes[**random**,3])^2))
    capacity <-c(capacity, node_demand)
    distance_sum <- c(distance_sum,distance)
}
global_hub_distance <- c(global_hub_distance,distance_sum)
capacity <- 0 
distance_sum <- 0 
}
min(global_hub_distance)
}