How to calculate sum of unique ways found in a distance matrx - r

Question

I have a data frame of 3 points in space represented by their longitude and latitute:
myData <- structure(list(lng = c(-37.06852042, -37.07473406, -37.07683313
), lat = c(-11.01471746, -11.02468103, -11.02806217)), .Names = c("lng",
"lat"), row.names = c(NA, 3L), class = "data.frame")
Next, I use the geosphere package to get a distance matrix (in meters, which I convert to km) for the points:
> m <- round(distm(myData)/1000,2)
> rownames(m) <- c("A", "B", "C")
> colnames(m) <- c("A", "B", "C")
> m
A B C
A 0.00 1.30 1.74
B 1.30 0.00 0.44
C 1.74 0.44 0.00
Given this is a distance matrix and I have 6 ways of going to A, B and C (like A -> B -> C, C -> A >-B, and so on), I would like to extract some information from it, like the minimum, the median, and the maximum distance.
To illustrate it, I calculated all the possible ways of my example manually:
ways <- c(abc <- 1.3 + 0.44,
acb <- 1.74 + 0.44,
bac <- 1.3 + 1.74,
bca <- 0.44 + 1.74,
cab <- 1.74 + 1.3,
cba <- 0.44 + 1.3)
> min(ways)
[1] 1.74
> median(ways)
[1] 2.18
> max(ways)
[1] 3.04
How do I automate this task, given that I'll be working with more than 10 locals and this problem has factorial complexity?

Answer 1

I wrote a package called trotter that maps integers to different arrangement types (permutations, combinations and others). For this problem, it seems that you are interested in the permutations of locations. One of the objects in the package is the permutation pseudo-vector that is created using the function ppv.
First install "trotter":
install.packages("trotter")
Then an automated version of your task might look something like:
library(geosphere)
myData <- data.frame(
lng = c(-37.06852042, -37.07473406, -37.07683313),
lat = c(-11.01471746, -11.02468103, -11.02806217)
)
m <- round(distm(myData) / 1000, 2)
locations <- c("A", "B", "C")
rownames(m) <- colnames(m) <- locations
library(trotter)
perms <- ppv(k = length(locations), items = locations)
ways <- c()
for (i in 1:length(perms)) {
perm <- perms[i]
route <- paste(perm, collapse = "")
ways[[route]] <- sum(
sapply(
1:(length(perm) - 1),
function(i) m[perm[i], perm[i + 1]]
)
)
}
Back in the R console:
> ways
ABC ACB CAB CBA BCA BAC
1.74 2.18 3.04 1.74 2.18 3.04
> # What is the minimum route length?
> min(ways)
[1] 1.74
> # Which route (index) is this?
> which.min((ways))
ABC
1
Just remember, like you said, you're dealing with factorial complexity and you might end up waiting a while running this brute force search with more than a few locations...