http://www.seas.harvard.edu daily 1 2008-12-03T05:00:50Z http://www.seas.harvard.edu/news-events/calendars/community/thanksgiving Thanksgiving Holiday No publisher mrutter 2009-06-26T18:15:21Z Event http://www.seas.harvard.edu/news-events/calendars/academic/thanksgiving-recess Thanksgiving recess for students No publisher mrutter 2009-06-26T19:09:16Z Event http://www.seas.harvard.edu/news-events/calendars/applied_physical_sciences/environmental_science/copy4_of_environmental-sci-eng-seminar-1 Dr. Abel Lau No publisher mrutter 2009-09-11T19:55:10Z Event http://www.seas.harvard.edu/news-events/calendars/csee/theory_of_computation/192304710 It's the end of the semester, and you need to store on a computer your N students' grades from the 3-element universe {pass, fail, borderline}. Via so-called arithmetic coding you can store them using the minimum number of bits, N(log_2 3) + O(1), but then to retrieve a grade you need to read all the bits. Or you can use two distinct bits per grade, but then you waste a linear amount of space. A breakthrough by Patrascu (FOCS 2008), later refined with Thorup, shows how to store the grades using the minimum number of bits so that each grade can be retrieved by reading just O(log N) bits. We prove a matching lower bound: To retrieve the grades by reading b bits, space N(log_2 3) + N/2^b is necessary. We also prove lower bounds for other fundamental data structure problems, including: storing a set so that membership queries can be answered efficiently, storing a bit-string so that prefix sums can be computed efficiently, and storing a string of brackets so that matching brackets can be found efficiently. Part of this work is joint with Mihai Patrascu No publisher admin 2009-11-24T08:29:05Z Event