 
Summary: I/Oalgorithms Spring 2006Project 3  Theoretical Homework
The goal of this project is to use the theoretical techniques we have discussed in the first part of
the course to design new algorithms and data structures. The project should be done in the same
groups as project 1 and 2. A report with the solutions is due on Friday May 26, 2006. Remember
to argue for correctness and complexity of each of your solutions. The evaluation of the project
will be part of the final grade.
Sorting
1. Design an I/Oefficient algorithm for removing duplicate from a multiset of N elements (you
can not assume the range of the elements is known); The output from the algorithms should
be the K distinct elements among the N input elements in sorted order, and the algorithm
should run in O max n logm n  K
i=1 ni logm Ni, n I/Os, where Ni is the number of copies
of the i'th elements in the input set.
(Hint: Use mergesort and remove duplicates as soon as they are found. Analyze the algorithm
by considering how many of the Ni copies of an element can be present after j merge steps.)
Searching
2. Design a linear space external data structure for the problem of maintaining a set of inter
vals I, such that given a query point x the number of intervals in I containing x can be
reported in O(log2
B N) I/Os. The structure should support insertion and deletion of intervals
