Checking if two time intervals overlap
The code looks well presented, and it's clear how it maps to the problem statement.

The one thing that's not well defined is how we deal with exact equality of times.  I'm assuming that intervals are always half-open (i.e. including the start time, but excluding the end time); it would be wise to add suitable comments to ensure that all readers agree on what's expected.



It's possible to simplify considerably, because in all cases we want (and none we don't), t1 ends after t2 begins and t2 ends after t1 begins, giving us a simpler expression:

t1.begin.isBefore(t2.end) &amp;&amp; t2.begin.isBefore(t1.end)




If the Interval class is under your control, consider making this method a public instance method of that class.  You might also want to check that the parameters are not null, if users might use that to indicate an empty interval:

if (t1 == null || t2 == null)
    return false;


(this latter is an argument against using an instance method, as then the caller would need to check t1 isn't null).