Group Records with Time Interval Overlap

In this article, we will explore a problem that involves identifying records in a dataset where their time intervals overlap. We’ll start by discussing the concept of overlapping intervals and how it can be represented mathematically.

What are Time Intervals?

A time interval is a range of dates within which an event or activity occurs. For example, if we’re tracking tasks with start and end dates, these dates represent the time interval for each task.

To visualize this concept, let’s consider a simple example:

Suppose we have two tasks: Task A starts on January 1st, 2022, and ends on January 15th, 2022. Task B starts on January 10th, 2022, and ends on January 20th, 2022. In this case, the time intervals overlap between January 10th and January 15th.

Representing Time Intervals Mathematically

To represent these time intervals mathematically, we can use a simple data structure like two dates: start_date and end_date.

Let’s denote the start date of an interval as s and the end date as e. For example, if we have an interval with start date January 1st, 2022 (s = “2022-01-01”) and end date January 15th, 2022 (e = “2022-01-15”), we can represent it as:

interval(s = "2022-01-01", e = "2022-01-15")

Finding Overlapping Intervals

To find overlapping intervals, we need to compare the start and end dates of each interval. If the start date of one interval is before the end date of another interval, then they overlap.

Here’s an example in R:

interval1 <- data.frame(s = "2022-01-01", e = "2022-01-15")
interval2 <- data.frame(s = "2022-01-10", e = "2022-01-20")

if (interval1$s <= interval2$e && interval1$e >= interval2$s) {
  # intervals overlap
} else {
  # no overlap
}

Grouping Overlapping Intervals

Once we’ve identified overlapping intervals, we need to group them together. This means combining the start and end dates of each overlapping interval into a single date range.

For example, if we have two overlapping intervals:

interval1: January 1st, 2022 - January 15th, 2022 interval2: January 10th, 2022 - January 20th, 2022

We can combine these dates into a single date range: January 1st, 2022 - January 20th, 2022.

Here’s an example in R:

interval1 <- data.frame(s = "2022-01-01", e = "2022-01-15")
interval2 <- data.frame(s = "2022-01-10", e = "2022-01-20")

combined_interval <- data.frame(
  s = min(interval1$s, interval2$s),
  e = max(interval1$e, interval2$e)
)

print(combined_interval)

Output:

s e 1 2022-01-01 2022-01-20

Grouping Records by ID with Overlapping Intervals

Now that we’ve identified overlapping intervals and grouped them together, we can apply this logic to our original dataset.

Suppose we have a dataset containing tasks with start and end dates:

To group these tasks by ID with overlapping intervals, we can use the dplyr library in R.

Here’s an example code:

library(dplyr)

df <- data.frame(
  ID = c(1, 1, 1, 2),
  w_from = c("2010-01-01", "2010-01-05", "2010-01-29", "2011-07-01"),
  w_to = c("2010-01-31", "2010-01-15", "2010-02-13", "2011-07-31")
)

df$w_from <- as.Date(df$w_from)
df$w_to <- as.Date(df$w_to)

# Group by ID and find overlapping intervals
df %>% 
  group_by(ID) %>% 
  arrange(w_from) %>% 
  mutate(
    group = 1 + cumsum(cummax(lag(as.numeric(w_to), default = first(as.numeric(w_to)))) < as.numeric(w_from))
  ) %>%
  ungroup() -> df_overlapping

Output:

This code groups the tasks by ID and finds overlapping intervals using the dplyr library. The group column indicates which group each task belongs to.

In the next section, we’ll explore some additional examples of finding overlapping time intervals in different contexts.

Last modified on 2023-10-18