simulating the time needed to look for sherd-links (joins)

sherdlinks-simulation.r

# simulating the time needed to look for sherd-links (joins)

# number of sherds
nos <- c(2^(4:16))

# simplistic model: look for links between any two sherds

dx0 <- choose(nos, 2)

# first realistic model: look for links only between sherds
# of the same class, assuming 5 equally abundant classes

m1.class <- 5

m1.fun <- function(n) sum(choose(rep(n%/%m1.class,m1.class), 2))
dx1 <- sapply(nos, m1.fun)

# second realistic model: as model 1, but with uneven frequency
# of classes, roughly as observed in some real assemblages

m2.classes <- c(0.35, 0.30, 0.20, 0.10, 0.05)

m2.fun <- function(n) sum(choose(m2.classes * n, 2))

dx2 <- sapply(nos, m2.fun)

# third realistic model: as model 2, but with random colors
# to help (e.g. you're not trying to link brown sherds with
# red ones

m3.classes <- m2.classes
m3.colors <- 2

m3.fun <- function(n) sum(choose(m3.classes / m3.colors * n, 2) * m3.colors)

dx3 <- sapply(nos, m3.fun)

# realistic models have values of about one quarter and less with
# respect to the simplistic model, it is a "slow" exponential growth

plot(nos, dx0, ylog=TRUE)
points(nos, dx1, col="red")
points(nos, dx2, col="blue")
points(nos, dx3, col="green")

grid()