CMSC-641 Algorithms: Assignments (Fall 1995)

Read and follow the homework guidelines.

Assignment 1 (due September 20): Algorithm Design and Analysis

  1. Solve Problem 1 from the Fall 95 PhD comprehensive examination in algorithms, which was passed out in class on September 11.

  2. Solve Problem 2 from the Fall 95 PhD comprehensive examination in algorithms. Also, solve the resulting recurrence.

  3. a) When a researcher presents a new algorithm, what are her responsibilities to her readers?

    b) Solve Problem 16.3-6* (longest monotonically increasing subsequence). Honor your responsibilities that you explained in part (a).

Assignment 2 (due October 4): Binomial and Fibonacci Heaps

  1. Problem 20-2
  2. Exercise 21.4-1
  3. Problem 21-1

Assignment 3 (due October 11): Average-case, Probablistic, and Amortized Analyses

  1. Exercise 6.2-5
  2. Problem 6-2
  3. Problem 18-3
  4. (Optional) Design a probablistic algorithm for ``unsorting any array.'' Precisely state and prove what effect your algorithm has on any input array of n integers.

Assignment 4 (due October 18): Union/Find

  1. Problem 22-1
  2. Problem 22-3
  3. Exercise 22.3-4

Assignment 5 (due October 25): Matroids, Randomly-built trees

  1. Problem 17-2
  2. Problem 13-3
  3. Problem 16-5

No homework due November 1, the date of Exam I.

Assignment 6 (due November 15): Network Flow

  1. Exercise 27.2-10
  2. Exercise 27.3-4
  3. Problem 27-1

Assignment 7 (due November 20): Network Flow, Sorting Networks

  1. Exercise 27.5-4
  2. Problem 27-5
  3. Problem 28-3

Progress report due on project by 12noon, November 22. See project description.

Assignment 8 (due November 29): NP-Completeness

  1. a) Briefly list and describe three major techniques for proving problems NP-complete. For each technique, what are important characteristics of a problem that suggest the technique is well-suited for the problem?

    b) Solve Problem 4 from the Fall 1995 Ph.D. Comprehensive Examination in Algorithms (see handout from HW 1). What technique seems most appropriate and why?

  2. Problem 36-2
  3. Problem 37-1

No homework due on December 6, the date of Exam II.