Group date intervals by the proximity of their start- and end-times - r

Question

Suppose I have a series of observations representing date intervals, e.g.
library(dplyr)
library(magrittr)
df <-
data_frame(start = as.Date(c('2000-01-01', '2000-01-03', '2000-01-08',
'2000-01-20', '2000-01-22')),
end = as.Date(c('2000-01-02', '2000-01-05', '2000-01-10',
'2000-01-21', '2000-02-10')))
I would like to group these observations such that the start time of observation n occurs within some specified interval following the end date of observation n-1. For instance, if we set that interval to be 5 days, we would see something like:
# start end group
# (date) (date) (dbl)
# 1 2000-01-01 2000-01-02 1
# 2 2000-01-03 2000-01-05 1
# 3 2000-01-08 2000-01-10 1
# 4 2000-01-20 2000-01-21 2
# 5 2000-01-22 2000-02-10 2
(For the sake of simplicity, I'm assuming no overlap in dates, although this isn't necessarily the case in the data). I thought about using igraph to create a weighted edgelist, but that seemed overly complicated. Efficiency is, I believe, important: I'll be running this on roughly 4 million groups of data of about 5-10 rows each.
While my solution does work, to me it seems error-prone, slow, and clunky. I'm thinking using a package or some vectorization would really improve matters.
group_dates <- function(df, interval){
# assign first date to first group
df %<>% arrange(start, end)
df[1, 'group'] <- 1
# for each start date, determine if it is within `interval` days of the
# closest end date
lapply(df$start[-1], function(cur_start){
earlier_data <- df[df$end <= cur_start, ]
diffs <- cur_start - earlier_data$end
min_interval <- diffs[which.min(diffs)]
closest_group <- earlier_data$group[which.min(diffs)]
if(min_interval <= interval){
df[df$start == cur_start, 'group'] <<- closest_group
} else {
df[df$start == cur_start, 'group'] <<- closest_group + 1
}
})
return(df)
}

Answer 1

You can do that relatively easily with dplyr.
The idea is the following:
Lag the end data (shifting it down by one)
Calculate the difference between start date and the lagged end date
Adding 'BreakPoints' - A variable with TRUE when the difference is more than 5 days and FALSE otherwise
Calculating the cumulative sum of this break-point. This will add 1 every time it find a new breakpoint so a new interval should be started
Something like this should work for you:
df %>%
mutate(lagged_end = lag(end),
diff = start - lagged_end,
new_interval = diff > 5,
new_interval = ifelse(is.na(new_interval), FALSE, new_interval),
interval_number = cumsum(new_interval))
This should be also quite quick since it's all in dplyr

Answer 2

This isn't as elegant as Lorenzo Rossi's solution, but offers a slightly different approach using cut.Date and 2 lines of code:
breakpoints <- c(FALSE, sapply(2:nrow(df), function(x) df[x,"start"] - df[x-1,"end"]) > 5)
clusterLabels <- as.numeric(cut.Date(df$start, c(min(df$start), df[breakpoints, "start"], max(df$start)+1)))