r - How to flatten / merge overlapping time periods

Question

I have a large data set of time periods, defined by a 'start' and and an 'end' column. Some of the periods overlap.

I would like to combine (flatten / merge / collapse) all overlapping time periods to have one 'start' value and one 'end' value.

Some example data:

  ID      start        end
1  A 2013-01-01 2013-01-05
2  A 2013-01-01 2013-01-05
3  A 2013-01-02 2013-01-03
4  A 2013-01-04 2013-01-06
5  A 2013-01-07 2013-01-09
6  A 2013-01-08 2013-01-11
7  A 2013-01-12 2013-01-15

Desired result:

  ID      start        end
1  A 2013-01-01 2013-01-06
2  A 2013-01-07 2013-01-11
3  A 2013-01-12 2013-01-15

What I have tried:

  require(dplyr)
  data <- structure(list(ID = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L), class = "factor", .Label = "A"), 
    start = structure(c(1356998400, 1356998400, 1357084800, 1357257600, 
    1357516800, 1357603200, 1357948800), tzone = "UTC", class = c("POSIXct", 
    "POSIXt")), end = structure(c(1357344000, 1357344000, 1357171200, 
    1357430400, 1357689600, 1357862400, 1358208000), tzone = "UTC", class = c("POSIXct", 
    "POSIXt"))), .Names = c("ID", "start", "end"), row.names = c(NA, 
-7L), class = "data.frame")

remove.overlaps <- function(data){
data2 <- data
for ( i in 1:length(unique(data$start))) {
x3 <- filter(data2, start>=data$start[i] & start<=data$end[i])
x4 <- x3[1,]
x4$end <- max(x3$end)
data2 <- filter(data2, start<data$start[i] | start>data$end[i])
data2 <- rbind(data2,x4)  
}
data2 <- na.omit(data2)}

data <- remove.overlaps(data)

Answer 1

Here's a possible solution. The basic idea here is to compare lagged start date with the maximum end date "until now" using the cummax function and create an index that will separate the data into groups

data %>%
  arrange(ID, start) %>% # as suggested by @Jonno in case the data is unsorted
  group_by(ID) %>%
  mutate(indx = c(0, cumsum(as.numeric(lead(start)) >
                     cummax(as.numeric(end)))[-n()])) %>%
  group_by(ID, indx) %>%
  summarise(start = first(start), end = last(end))

# Source: local data frame [3 x 4]
# Groups: ID
# 
#   ID indx      start        end
# 1  A    0 2013-01-01 2013-01-06
# 2  A    1 2013-01-07 2013-01-11
# 3  A    2 2013-01-12 2013-01-15