Finding (number of) overlaps in a list of time ranges

Question

Given a list of time ranges, I need to find the maximum number of overlaps.

Following is a dataset showing a 10 minute interval of calls, from which I am trying to f

Answer 1

How about a naive approach:

• Take the least of the start times and the greatest of the end times (this is your range R)
• Take the shortest call duration -- d (sorting, O(nlog n))
• Create an array C, of ceil(R/d) integers, zero initialize
• Now, for each call, add 1 to the cells that define the call's duration O(n * ceil(R/d))
• Loop over the array C and save the max (O(n))

I guess you could model this as a graph too and fiddle around, but beats me at the moment.