UMBC CMSC441H, Design & Analysis of Algorithms, Spring 2005, Honors Section

Homework Assignments

Homework 1, Due Tuesday 02/08

1. Chapter 1, Exercise 1 (page 22).
2. Chapter 1, Exercise 6 (page 25).
3. Chapter 1, Exercise 8 (page 27).

Homework 2, Due Tuesday 02/15

1. Chapter 2, Exercise #3 (page 64).
2. Chapter 3, Exercise #4 (page 102).
3. Chapter 3, Exercise #8 (page 103).

Homework 3, Due Tuesday 02/22

1. Chapter 3, Exercise #9 (page 104).
2. Chapter 3, Exercise #12 (page 106).
3. Chapter 4, Exercise #5 (page 180). Prove that your algorithm is correct.

Homework 4, Due Thursday 03/03

1. Chapter 4, #3 (page 179-180).
2. Chapter 4, #4 (page 180).
   Note: Briefly argue that your algorithm is correct and justify the running time of your algorithm.
3. Chapter 4, #16 (page 186-187).
   Note: Prove that your algorithm provides the optimum solution. State and briefly justify the running time of your algorithm.

Homework 5, Due Thursday 03/10

• Describe your algorithm at a high level using English sentences.
• Avoid code and pseudo-code (definitely not a substitute for descriptions in English).
• Justify that your algorithm actually does what is intended.
• State and justify the running time.

1. Chapter 4, #2 (page 179).
2. Chapter 4, #17 (page 187).
3. Chapter 4, #20 (page 189).

Homework 6, Due Thursday 03/17

1. Solve each of the following recurrence relations using either iteration (expand until you see a pattern) or substitution (guess and prove by induction). Show all work. Finally, check your answer using the Master Theorem, if it is applicable.
   1. T(n) = T(n/4) + n²
   2. T(n) = T(sqrt(n)) + 5
   3. T(n) = 4 T(n/3) + n log n
2. Chapter 5, #2 (page 232).
3. Chapter 5, #3 (page 233).

Homework 7, Due Tuesday 04/05

1. Chapter 6, #4 (page 297).
2. Chapter 6, #6 (page 299-300).
3. Chapter 6, #16 (page 308-309).

Homework 8, Due Tuesday 04/12

1. Chapter 6, #23, page 313.
   
   
2. Chapter 7, #11, page 395. Note: The parenthetical remark

   ... (regardless of how it chooses its forward-edge paths).

   in the statement of the claim is critical in the interpretation of this question.
   
   
3. Chapter 7, #14, page 396.

Homework 9, Due Tuesday 04/19

1. Chapter 7, #9 (page 394).
2. Chapter 7, #17 (page 398).
3. Chapter 7, #19 (page 400-402).

Homework 10, Due Tuesday 04/26

1. Chapter 6, #8 (page 301-302).
2. Chapter 7, #16 (page 397-398).
3. Chapter 8, #5 (page 479). Hint: reduce from 3SAT.

Homework 11, Due Tuesday 05/03

1. Chapter 8, #7 (page 480).
2. Chapter 8, #8 (page 480-481).
3. Chapter 8, #9 (page 481).

Homework 12, Due Tuesday 05/12

1. Chapter 11, #1 (pages 614).
   Hint: if a and b are integers and a < 2b, then a + 1 ≤ 2b.
2. Chapter 11, #5 (pages 616-617).
   Hint: you must redefine the load on a machine to take into account of slow and fast machines. Also, the algorithm in Section 11.1 must be modified so the load between slow and fast machines are balanced.
3. Chapter 11, #10 parts a & b (pages 619-620).

Homework 13, Due Tuesday 05/17

1. Chapter 13, #1 (page 737).
2. Chapter 13, #2 (page 737-738).
3. Chapter 13, #3 (page 738-739).