Overview. Algorithm design and analysis is fundamental to all areas of computer science and gives a rigorous framework for the study optimization other disciplines. This course provides an introduction to algorithm design through a survey of the common algorithm design paradigms of greedy optimization, divide and conquer, dynamic programming, network flows, and randomized algorithms. Important themes that will be developed in the course include algorithmic abstraction-design-analysis process and computational tractability (e.g., NP-completeness).

Prerequisites. EECS 310 (Mathematical Foundations of Computer Science) and EECS 311 (Data Structures and Data Management) which cover abstract data types such as stacks, queues, and binary search trees; and discrete mathematics such as recurrence relations, sets, and graphs.

Grading. 60% Problem sets, 20% Midterm, 20% Final, 3% classroom participation (bonus).

Homework Policy. Homeworks may be done in pairs. Both students must contribute to the solution of all problems. One copy of the assignment should be turned in with the names of both students on it. Both students will receive the same grade. You may consult your text book and course notes when answering homework questions; you must not consult the Internet. Homeworks are assigned in class and due on Thursday the week after (or as noted). Late homework will be accepted until Friday at 5pm and will be marked down by 25%. You may replace one low homework grade by completing a programming project that implements an algorithm related to the assignment, subject to pre-approval by the instructor.

Tentative Schedule:

• Jan. 5: Course overview, algorithmic abstraction-design-analysis paradigm, and the stable matching problem. (Chapter 1)
• Jan. 7: Review of runtime analysis, graphs, and basic graph algorithms. (Chapters 2 and 3)
• Jan. 12: Greedy algorithms: interval scheduling. (Chapter 4)
• Jan. 14: Greedy algorithms: minimum spanning trees, matroids. (Chapter 4)
• Jan. 19: Greedy algorithms: shortest paths, MSTs. (Chapter 4)
• Jan. 21: Divide and conquer: merge sort, recurrence relations, public key cryptography, repeated squaring (Chapter 5)
• Jan. 26: Divide and conquer: integer multiply, convolution, fast Fourier transform (Chapter 5)
• Jan. 28: Dynamic programming: memoization, weighted interval scheduling, integer knapsack (Chapter 6)
• Feb. 2: Dynamic programming: all pairs shortest paths (Chapter 6)
• Feb. 4: Reductions, Network flow, Bipartite Matching (Chapter 7)
• Feb. 9: MIDTERM.
• Feb. 11: Network flow. (Chapter 7)
• Feb. 16: NP and intractability: NP, polynomial time reductions decision problems. (Chapter 8)
• Feb. 19: NP and intractability: NP, circuit sat, 3-sat. (Chapter 8)
• Feb. 23: NP and intractability: circuit sat, 3-sat, independent set. (Chapter 8)
• Feb. 25: Approximation algorithms: TSP, metric TSP, knapsack (Chapter 11)
• Mar. 2: Approximation algorithms: pseudo polynomial time, PTAS, knapsack (Chapter 11)
• Mar. 4: Randomized algorithms: global min cut (Chapter 13)
• Mar. 9: Online algorithms: ski-renter.
• Mar. 11: FINAL (cummulative).