Course Info

• Instructor: Hamid Zarrabi-Zadeh
• Course Syllabus
• Course Calendar
• Quera Page (Assignments, Announcements)

Lectures

• Introduction (Mehr 3, 8)
• Analysis of Algorithms, Fibonacci Numbers [KT Ch2]
• Sample Problems: Largest Consecutive Subsequence, 3SUM
• Design by Induction (Mehr 10)
• Evaluating Polynomials, Finding Celebrity, Finding Min-Max [M Ch5]
• Divide and Conquer (Mehr 15, 17)
• Exponentiation, Computing Recurrences, Integer Multiplication, Closest Pair [KT Ch5.1-5]
• Matrix Multiplication, Fast Fourier Transform [CLRS Ch4.2], [KT Ch5.6]
• Greedy Algorithms (Mehr 22, 24)
• Coin Changing, Activity Selection, Knapsack [KT Ch4.1-2]
• Data Compression, Shannon-Fano, Huffman Codes [KT Ch4.8]
• Dynamic Programming (Mehr 29, Aban 1, 6)
• Computing Binomials, Weighted Interval Scheduling [KT Ch6.1-2]
• Matrix-Chain Multiplication, Knapsack, Independent Set on Trees [CLRS Ch14.2], [KT Ch6.4]
• Largest Common Subsequence, Edit Distance, LIS [CLRS Ch14.4], [M Ch6.11]
• Graph Algorithms (Aban 8, 13, 15, 20)
• Graph Traversals: BFS and DFS, Applications [CLRS Ch20.1-5]
• Minimum Spanning Trees: Kruskal, Prim, and Boruvka [KT Ch4.4], [CLRS Ch21]
• Binomial Heaps, Fibonacci Heaps [CLRS 3e Ch19]
• All-Pairs Shortest Paths: Floyd-Warshal and Johnson [CLRS Ch23]
• Maximum Flow (Aban 27, 29)
• Max Flow and Min Cut, Ford-Fulkerson Algorithm [KT Ch7.1-2]
• Variants and Applications of Maximum Flow [KT Ch7.5-8]
• String Matching (Azar 4, 6)
• Knuth-Morris-Pratt Algorithm [CLRS Ch32]
• Rabin-Karp Algorithm, Fingerprint Method [CLRS Ch32]
• Linear Programming (Azar 11, 13)
• Definition and Applications [CLRS Ch29.1-2]
• Simplex Method [CLRS 3e Ch29.3, 5]
• NP-Completeness (Azar 18, 25, 27)
• Polynomial-Time Reduction [KT Ch8.1-2]
• Circuit SAT, NP-Hardness [KT Ch8.3-4]
• Sequencing, Partitioning, and Numerical Problems [KT Ch8.5,7,8]
• Backtracking (Dey 2, 4)
• n-Queens, Subset Sum, 3-Coloring [BB Ch6.6]
• Branch and Bound, Coloring, TSP, Game Trees, α-β Pruning [BB Ch6.6]
• Approximation Algorithms (Dey 9, 11)
• Vertex Cover, Max Cut [CLRS Ch35.1], [KT Ch12.4]
• TSP, Hardness of Approximation [CLRS Ch35.2], [KT Ch11.6]

References

• [CLRS] T. Cormen, C. Leiserson, R. Riverst, and C. Stein. Introduction to Algorithms. 4th edition, MIT Press, 2022.
• [KT] J. Kleinberg and E. Tardos. Algorithm Design. Addison Wesley, 2005.
• [M] U. Manber. Introduction to Algorithms: A Creative Approach. Addison Wesley, 1989.
• [BB] G. Brassard and P. Bratley. Algorithmics: Theory and Practice. Prentice-Hall, 1988.

Resources

• Lecture Slides for Algorithm Design, by Kevin Wayne