IAI

Course Objective:

The course introduces the basics of computational complexity analysis and various algorithm design paradigms. The goal is to provide students with solid foundations to deal with a wide variety of computational problems, and to provide a thorough knowledge of the most common algorithms and data structures. After the course, a student should be able to analyze the asymptotic performance of algorithms, write rigorous correctness proofs for algorithms, and apply important algorithmic design paradigms and methods of analysis.

Syllabus:

• Introduction: Algorithm, Instance of a problem, Efficiency of algorithm, Growth of Functions, Asymptotic notation, Worst case, Best case, Average Case time complexity, Substitution method, Recursion tree method, Masters Theorem.
  
• Elementary Data Structure: Array, Linked list, Stack, Queue, Heap, Binary Search Tree, AVL Tree, Hash table, Disjoint Set Data Structure.
  
• Searching, Sorting and Order Statistics: Linear and Binary Search, Heap Sort, Quick Sort, Sorting in linear time, Order statistics, Finding Median in linear time.
  
• Divide and Conquer Paradigm: Merge Sort, Counting Inversion, Closest Pair of Points.
  
• Greedy Algorithms: Interval Scheduling Problem and its variants, Optimal Caching Problem, Minimum Spanning tree Problem, Huffman
  Code, Clustering Problem, Fractional Knapsack problem, Dijkstra Algorithm.
  
• Dynamic Programming: Matrix Chain Multiplication, Longest Common Subsequence, Optimal Binary Search Tree, Segmented Least Square Problem, 0/1-Knapsack Problem, Subset Sum Problem, Bellman Ford Algorithm.
  
• Graph algorithms: BFS, DFS, Floyd Warshall, Fold Fulkerson.
  
• Number Theoretic Algorithms: Euclidean, Extended Euclidean, CRT, Pollard Rho.
  
• Advanced Topics: P, NP, NPC (Circuit Satisfiability, Vertex Cover, Graph Coloring), Approximation Algorithm of some NPC Problems, Probabilistic Algorithm: Miller Rabin Primality Algorithm.
  
  

References:

[1] T. H. Cormen, C. E. Leiserson and R. L. Rivest: Introduction to Algorithms, PrenticeHall of India, New Delhi, 1998.
[2] J. Kleinberg, E. Tardos: Algorithm Design, Pearson Education, 2006.
[3] A. Aho, J. Hopcroft and J. Ullman: The Design and Analysis of Computer Algorithms, A. W. L, International Student Edition, Singapore, 1998.
[4] E. Horowitz, S. Sahni, S. A. Freed: Fundamentals of Data Structures in C, 2008.
[5] S. Baase: Computer Algorithms: Introduction to Design and Analysis, 2nd ed., Addison-Wesley, California, 1988.

Classes (by Dr. Nilanjan Datta):

• Introduction to Algorithms, Insertion Sort, Correctness using Loop Invariants, Analysis of Algorithms: Best Case, Average Case, Worst Case Analysis. [Class 1]
  
  
• Growth of Function, Asymptotic Notation, Introduction to Data Structures, Difference between Interface and Data Structure, Static Sequence Interface, Static Array. [Class 2]
  
  
• Dynamic Sequence Interface, Dynamic Array, Linked List, Doubly Linked List, A comparative study of Static Array, Linked List, and Dynamic Array with respect to the efficiency of different static and dynamic operations. [Class 3]
  
  
• Data Structures to represent Polynomials; Stack Data Structure and Its applications: Infix to Postfix Conversion, Evaluation of Postfix expression, Finding Minimum elements in the stack efficiently. [Class 4]
  
  
• Queue, Circular Queue, Priotity Queue, Heap Data Structure, Max-heap, Min-heap, Heap Sort, Implementation of Priority Queue using Heap. [Class 5]
  
  
• Fibonacci Heap, Priority Queue using Fibonacci Heap; Searching: Linear and Binary Search, Binary Search Tree, Motivation for Balanced Binary Search Tree. [Class 6]
  
  
• Balanced Binary Search Tree, AVL tree, Red-Black tree. [Class 7]
  
  
• Quick Sort, Randomized Quick Sort, Expected Running Time of Randomized Quick Sort, Comparison based Sort, Decision Tree, Lower Bound on Comparison based Sort. [Class 8]
  
  
• Sorting in Linear Time: Counting Sort, Stable Sort, Radix Sort, Bucket Sort. [Class 9]
  
  
• Medians and Order Statistics: Minimum and Maximum, Selection in expected linear time, Selection in worst case linear time. [Class 10]
  
  
• Dynamic Sets with Dictionary Operations: Direct Address Table, Hash Table, Collision Resolution by Chaining, Open Addressing: Linear and Quadratic Probing, Perfect Hashing. [Class 11]
  
  
• Dynamic Programming: Optimal Binary Search Trees, Coin Game. [Class 12]
  
  
• Graph Algorithms: Representation, BFS, DFS. [Class 13]
  
  
• Randomized Algorithms and Probabilistic Analysis. [Class 14]
  
  
  

Classes (by Prof. Rana Barua):

• Divide and Conquer Paradigm: Merge Sort, Counting Inversions, Closest Pair of Points. [Class 1]
  
  
• Greedy Algorithms (part I): Interval Scheduling Problem – EFT Algorithm, Minimum Spanning Tree Construction – Prim’s Algorithm. [Class 2]
  
  
• Greedy Algorithms (part II): Minimum Spanning Tree Problems: Prim’s Algorithm, Kruskal’s Algorithm, Use of union-find data structure, Clustering Problem. [Class 3]
  
  
• Greedy Algorithms (part III): Clustering Problem, Huffman Coding. [Class 4]
  
  
• Greedy Algorithms (part IV): Huffman Algorithm, Fractional Knapsack, Single-source Shortest Path, Dijkstra’s Algorithm. [Class 5]
  
  
• Dynamic Programming (part I): Longest Common Sequence, Matrix Chain Multiplication. [Class 6]
  
  
• Dynamic Programming (part II): Matrix Chain Multiplication, Subset Sum and Knapsack. [Class 7]
  
  
• Number Theoretic Algorithms (part I): Euclidean, Extended Euclidean, Chinese Remainder Theorem. [Class 8]
  
  
• Number Theoretic Algorithms (part II): Pollard’s Rho Factoring Algorithm, Miller-Rabin Algorithm for Primality Testing. [Class 9]
  
  
• Miller-Rabin Algorithm for Primality Testing (contd), Turing Machine, NP-Complete Problems [Class 10]
  
  
• NP-Complete Problems: Circuit Satisfiability, Vertex Cover, Graph Coloring. [Class 11]
  
  

Notes (by Prof. Rana Barua):

• [Divide and Conquer]
  
  
• [Greedy Algorithms] (Updated)
  
  
• [Sorting and Searching II]
  
  
• [Dynamic Programming]
  
  
• [Number Theory]
  
  
• [Basics of Turing Machine]