Advanced Perl Programming, otherwise known as the Panther book from O'Reilly & Assoc. has a discussion that you would probably find beneficial. Chapter two, section three:

Consider that there are only 24 * 7 = 168 hours in a week, the entire week's schedule can be represented by a bitmap vector of 21 bytes (168 / 8) .... The other cool thing is that you can obtain time conflicts by logically AND-ing two bitmaps.

The implementation example provided in the book uses vec to construct the bitmaps, and logical 'and' to check for overlaps.

Hope this helps...