Work Note 9, DM803, fall 2016

Exercises November 10

1. If you were to implement cuckoo hashing, you would of course like to fine-tune the idea. Other than choices of the constants involved such as ε, c, etc., which possible variants of the basic idea could one consider? No analysis expected here!
2. For this exercise, recall the material on universal and perfect hashing. We want to remove duplicates from a collection of elements S of size n to form S' of size n' in expected time O(n) under the constraints given below (one at a time). Suggest (increasingly complex) solutions for the three cases.
   1. Space O(n).
   2. Space O(n') where n' is known.
   3. Space O(n') where n' is unknown.
3. I will lecture on the topic of properties of hashing that I didn't manage to cover at the lecture [LN-Hash].

Lecture November 14

• Van Emde Boas Trees [F03].
• X- and Y-Fast Tries [W83].