v22.0310-003: Homework 6

Due date: Thursday December 16 (before 11pm). If you stuff under my door, be sure to place it in an envelop with your name.

This last homework is OPTIONAL. Only do it if you think you need extra credit to boost your grades. It has only a written part.

Look here for additional information after the original posting of assignment:
  1. Exercise 10.14 (Page 331). Double hashing.

  2. Exercise 11.9 (Page 360). Insertion into a 2-3 tree.

  3. What is the advantage of B+-trees over B-trees?

  4. Suppose each key takes 10 bytes and each pointer takes 4 bytes. Let T be a B-tree of order m where each node of a B-tree has 512 bytes. Determine the maximum value of m.

  5. Exercise 13.5 (pagte 417). Splay tree searching.

  6. Is it true that splaying a tree always reduce its height? If so, argue why. If not, give a counter example.

  7. Reduce the problem of Hamiltonian Cycle to the Traveling Salesman problem. See p.459, exercise 15.5 for a definition of Hamiltonian cycle.
    CLARIFICATION: I mean, do exercise 15.5. This amounts to reducing Hamiltonian Cycle to Traveling Salesman.

  8. Exercise 15.3 (page 459), multiplying matrices.
  9. RECOMMENDED EXTRA PROBLEMS: Do not hand in, as they will not be graded.
    1. Write a Java program to rotate a node. Assume that each node has three references, point to its parent, its left and right child.

    2. Exercise 11.15 (page 361). Min and Max number of records in B+ tree.

    3. Show that the problem of Vertex Cover is in NP. See p.459, exercise 15.6 for a definition of Vertex Cover.